BSchroe,
ALL that I can tell you about that precise subject is that 3-4 years ago, during a "question & answer period" after one of the TX history seminars, the curator of our Witte Museum said that: BLADES were more often carried "in town" by early Texicans than any sort of firearm.
(NO quotation marks, as I didn't write down his exact words but that is close to his actual comment.)
Period information about COL Bowie, when he was in TX, do NOT indicate that he carried any sort of pistol inside Bejar, though he was never known to be without "My little friend" (His about 4-inch bladed dagger that his cousin Nellie gave him) AND his famous (or NOTORIOUS, if you prefer) fighting knife.
Given that he had all of the Veramendi money behind him, he COULD have bought most any firearm(s) (and/or anything else that he chose to buy) that he chose, had he desired one or more handguns.
yours, satx