First, I do not know firsthand if the train to St. Jean waits for incoming trains. I do know that French trains are deadly on time. The station in Bayonne is medium size and has several platforms. The high speed TGV train will arrive at one platform; the train to St. Jean has its own track because it is a two-car regional train (usually), and will leave from another. I do not remember if changing platforms requires using an underground tunnel. Many stations in France have these tunnels, and if you are on the wrong platform, it takes a bit of time to get to another one, even in smaller stations.
For your peace of mind, I suggest that you contact the station or TGV. While it makes sense for the departing train to wait for one arriving at the same time, I have found that France is very rule oriented, and also they are quite proud that their trains run on time. If the schedule says 1829, I personally would expect the train to depart at that time unless the authorities told me otherwise. On the other hand, I don't see any trains from Paris arriving at 1829, so you might double check that arrival time. If you are on the 1708, you will have plenty of time.