Chords in ‘flat’ keys tend to be limited to the same old movable shapes that you’ve seen before, but you can find some exceptions if you’re crafty.
Here's the standard Bb barre we all know and love.
Here’s another chord using the same shape as Bm11 and G6add9 (no 3rd). This one will also work together with the G.
This one’s a bit more mysterious-sounding and has a couple of open strings, unusual for a Bb chord. Be careful, however, as the #11 could easily clash with other chords in a song.
This chord’s upbeat sound is reminiscent of Gypsy jazz or western swing. It works well as an arpeggio, too.