However something I have learned about the law is the law itself is rarely complete, because case law can make the law actually mean something even contrary to what it says in statute alone.
It can make it more detailed, apply or not apply in various situations not listed in statute, or even make the statute mean the opposite of what it appears to say in rare cases (have run across this in California when looking up laws and the case law that defines them.)
So you would need to also know relevant case law, along with any additional exemptions.
However Texas allows everyone to keep a loaded firearm with a motor vehicle.
It would appear to me this would include in the passenger compartment of the motorcycle, and especially within any portion of the vehicle. A saddlebag, or a tank bag, or anything else should be perfectly legal while riding.
It may even extend to the person's body, as a concealed firearm is legal within the passenger compartment of a vehicle in Texas.
But if it was, that protection would cease when you stepped off the bike. Meaning the transition from legal on the bike, to legal off the bike could be problematic if you chose to carry in such a manner, like when stopping at a gas station.