I think it was most likely because he didn't want to blow his cover. If he had gone up to the Narnians, the Calormenes would see it as well. And since he had no guarantee the Narnians would/could help before the Calormenes caused some harm, he didn't want to risk it.

~Riella

Keep in mind that this was in a very busy market place of Tashbaan, and a Horse that was moving its lips to communicate could still be seen by many Calormenes all around.

I guess Bree could follow the Narnians back to where they were staying, but wouldn't that seem kind of unusual for a seemingly dumb Horse to walk alongside humans with no lead?

I guess it also seems odd to me that people in Tashbaan would be so freaked out by seeing a horse talk, but not by a talking raven or a faun.

You answered why in your post:

Bree had no intention of letting all the crowd know that he could talk.

A horse breaking away from the crowd and running right up to a person in the procession would no doubt be suspicious. And also, people would be able to see him looking like he was talking and the Narnians talking back even if they couldn't hear what was being said.

Also, what good would that have done? The Narnians couldn't have taken Bree with them without people seeing the "great war horse". At this point, the Narnians were not yet expecting to sneak away. No doubt they would have been sent off with fanfare and trumpets and a procession down to the docks when they set off. Someone would be bound to recognize that Bree was a war horse and there might even be someone who would recognize whose horses it was.
On top of that, it is not said whether or not the Narnians brought horses with them but I'm pretty sure they didn't. They would have anything they needed provided by the Calormenes. And a horse is not exactly something you can sneak on board a ship easily.

Say Bree did run up to the Narnians and the Narnians decided to try to buy him back. How would they accomplish that? If I were a Calormene, I would be thinking what is so special about this horse? Why do they want it so badly? There must be something that makes them want this horse so badly and would start probing to try to find the answer. If the Narnians said he was a talking Narnian horse, you're back to square one and the Calormenes wouldn't sell him because they'd be able to make tons of money off of him. I personally would not buy a story of someone just "taking a fancy" to that particular horse.

Even if the Calormene's sold him without knowing he talked, how would they get him back to Narnia? They can't take him on the royal ship. Someone would have to ride him across the desert and back to Narnia. Seems like a lot of pains to take for a horse, even a good horse. I would be suspicious and wondering why they're taking such pains for a horse when they probably have dozens in Narnia and can buy a bunch at once from somewhere and have them shipped on a livestock boat whenever.

narnian_at_heart,

Bree should run up to the Narnians and say, "Help, I'm a talking horse trying to get back to Narnia." I don't see why there would be any need to buy Bree back. Bree's owner is miles away. I also don't see why any of the people in Tashbaan would care if some random horse off the street went with the Narnians.

I can't imagine the Narnians saying "sorry, we can't take you on board the ship. Looks like you're stuck here."

I also don't see why it is such a big deal that Bree can talk. The Narnians have a talking raven and a faun with them, but the people of Tashbaan don't seem alarmed and don't try to "make a show of them at fairs" or anything.

I guess it also seems odd to me that people in Tashbaan would be so freaked out by seeing a horse talk, but not by a talking raven or a faun.

They aren't just any talking raven or faun though. They are part of the official Narnian ambassadorial party. Calormenes expect odd things like that from the barbarians of the North. Bree, on the other hand, is for all intents and purposes in this situation a Calormene horse. To hear a Calormene horse talk would certainly cause a stir.

As to having a faun and talking raven, they are indeed a part of the ambassadorial party, but I don't think that they ever left their place of dwelling...

Calormenes expect odd things like that from the barbarians of the North. Bree, on the other hand, is for all intents and purposes in this situation a Calormene horse. To hear a Calormene horse talk would certainly cause a stir.

I dunno, I'm not quite seeing it. I guess I imagine it going something like this...

"Whoa! You can talk?!!"

"Yes...I'm from Narnia."

"Oh, okay."

narnian_at_heart,
I also don't see why it is such a big deal that Bree can talk. The Narnians have a talking raven and a faun with them, but the people of Tashbaan don't seem alarmed and don't try to "make a show of them at fairs" or anything.

First of all, how do you know the common folk of Tashbaan weren't taken aback by the faun and the talking raven? That could have been left off page.

Secondly, they couldn't possibly make a show of them at fairs. Tumnus and the Raven were under Edmund and Susan's protection.

I've always thought that the reason that Bree and/or Hwin (don't leave her out) didn't speak was because, they had pledged to go north with Aravis. If either had spoken, the horses would have gotten away and Shasta's story might have even come out right then, but the Narnians wouldn't have been able to do anything for Aravis and she would have been shipped back home and married off to someone that she didn't want to marry. If the Narnians HAD taken Aravis with them, then in the eyes of the Calormen, they would have been kidnapping her (even though she wanted to escape from Calormen) and it would have possibly started a war. Remember, at that point in time, we didn't know that Rabadash wanted to start a war anyway.

So, no - it's really understandable why neither of the horses spoke. It would have left Aravis in a real pickle and could have had dire results for Shasta as well. Besides, if they had spoken, Aravis would have never overheard Rabadash's plans and Shasta would not have saved Archenland and Narnia from their great danger - so, Aslan was ultimately behind the horses remaining silent.

Well Bree has been "dressed" as a Calormene horse, and the others were as well (dressed as Calormenes.) There is the chance they could be mistaken for spies, as Narnian/Calormene relations have always been shaky at best.

Also it may have been a matter of pride (after all Bree was a very prideful horse) and deep down inside, whether he realized it or not, he did not want to admit that he made the mistake of traveling to close to the border. He could admit it to Shasta because he was only a lowly poor boy, but otherwise he'd be admitting it to more respected people. And he may be fearful of embarrassing himself. As a result he came up with the excuse that they'd try to capture him and treat him as a circus freak. Related to this he may well have been content for the four of them to worry about themselves (believing "they could handel it").

Thirdly though he would have known them too be royalty, because of the criers. He was probably captured during the early days of the Pevensie reign and as a young foal. Would he have placed as much trust in them as those who had lived there all their lives?

I'm wondering why no one (or maybe I missed it) had mentioned Hwin. After all she was with them and could have said something too. Perhaps it was due to the first reason, or due to her shyness.

Or perhaps they were protecting Aravis. People may well have recognized her and known she had run away. If they had said something they risked exposing her, and there was no guarentee the Narnians could or would help her escape what the Calormenes would consider her royal and womanly duty. They risked creating an international incident.

Finally they may all simply have been scared. After all who acts logically in fear?

Or perhaps they were protecting Aravis.

This is by far my favorite proposed reason. Aravis being recognized was one of their biggest concerns. I can swallow that.

Yeah, I figured it was to protect Aravis. Even though it was terrible that she was being forced to marry, I don't know if the Narnians would let her come to Narnia with them. I can imagine them wanting her to make peace with her father.
For another thing, Bree may not have expected the Narnians to help him since he ran away. He didn't fully understand Narnian customs (which is obvious because of his misconception of Aslan) just like Shasta, who grew up in Calormen. Shasta expected the Narnians to kill him if he told them he wasn't Cor and would sell Aravis or send her back to her father. Bree might have thought the same thing.