Either on Bb trumpet or the Bb trombone, the transposition from C instrument music (concert key) is a snap. First, change the signature of the C instrument music by adding 2 sharps, each sharp negating a flat if they exist in the key the C music is written in. Once this is done, you then just play 2 half steps higher, as example a B would become a C# and it doesn't matter as there is no difference whether you are playing a Bb trumpet or Bb trombone. The method is the same!
NO, you cannot use a trumpet mpc to play your trombone or vice versa ... their shanks are NOT the same. Even if you had custom mpcs made, you must expect the tone to be different. I did recently acquire one of Ivan's Holton cornets with modified receiver to accept a trumpet mpc, and the change in tone is still something that is difficult for me to be familiar with.
PS: I've been transposing piano music (concert key music) since near the time I acquired my first trumpet in public school. Mainly such was all that was then available to me during the tail end of WWII and too was mostly from my Mother's and Grandmother's collections. I now have the remnants of their collections, inclusive now of some of the pops of the 50s I bought for my Mother. Added to such, is that I've scrounged from estate sales and thrift stores, each at costs as low as a nickel. Sadly, most is still in still in unpacked boxes we brought here in 2008 as are not archival acid free. I just hope the yard bag liners that I sealed will help preserve them. One of my prized recordings is my multi-brass instrument renditions of 2 of my Mother's "show off" piano songs, "Red Wing" and "Under The Double Eagle". Yeah, Mom played piano as well as a Pro IMO.