I've got five drill chucks for the Bridgeport. Four of those were new Jacobs (1 x 1/4", 2 x 3/8" and 1 x 1/2" ) and are on quick change arbors, so I don't need to remove the R8 collet each time. They also get used on the R8 CNC mill. I also have a Jacobs drill chuck on an R8 arbor that came with the Bridgeport.
I don't mess about sharing tooling on mill and lathe. I have two separate drill chucks on 3MT for the lathe. One came with the lathe, now too worn to be useful, and another, larger one, bought secondhand on Ebay.
All my drill chucks are keyed. When not in use the keys are stored in the chuck, so I don't lose them.
I also have an R8 to 3MT adaptor for Morse taper drills on the Bridgeport, but things can get short on headroom at times, 19" can get eaten up pretty quickly. In general I don't use drills bigger than 1" on the Bridgeport.
Andrew