I Never really got into using tabs, I learned to play by ear and that's how I learn new material, but I have been using sheet music to learn certain parts of new material. This may be of interest, I get most of my sheet music from "Musescore" this site provides free sheet music for a variety of genre's, it also allow you to transpose any song and print copies. Of all the material I play I usually print copies in a number of different keys, this enable me to learn to play a song in different keys on my C chrome.
As I see it, if you are using a Bb chrome and you want to play a piece in Bb it's pretty easy to do, just use sheet music in the key of C, basicly pretending you are on a C chrome. However, if you want to play a song written in Bb on a Bb chrome I still think you will still be playing in the tonic, but you would need to understand the note layout of the Bb chrome in order to read and play the sheet music. I do use chromes in different keys occasionally, but rarely play in the tonic, when I do I'm using sheet music written in C.