Making a call on a few of these:
Ted Washington: Bill first
Nate Clements: definitely Bill first
Pat Williams: tie between Bills/Vikings
Antoine Winfield: Viking first, barely
Jabari Greer: tie between Bills/Saints
Takeo Spikes: tie between three teams
London Fletcher: tie between three teams
None of these guys were known decidedly for their tenure with other teams, more so than the Bills, which I thought was the spirit of the thread. Bryce Paup, Chris Spielman and James Lofton would be the best examples of the type of player the OP was looking for, in my opinion.
Actually, upon further review, Paup might be best known as a Bill. Played three years here, as opposed to five in Green Bay, but had BY FAR his best seasons with the Bills.