2...d6 is 3...e5 is a very strong plan that should be recognised - and maybe met via 3. d4. In fact after 1 or 2...d6, black already demonstrates an understanding of white's plan and shows an active refutation attempt. (I'm very afraid to see the move in fact, but nobody in blitz ever tried it.) In any case, 2. b3 seems a very slow plan.
1...c5 is perfectly fine. It tempts white into 2. f4!? d5! (The Tal Gambit, strong against the old Grand Prix) 3. Nf3!? (The Bryntse Gambit as analysed in Mackenzie's blog.) 1. f4 c5 2. Nf3 d5 3. e4!? is another sequence. Personally I enjoy the resulting positions as white, both with and without the queen sac.
I played the Bird (Antoshin to be exact) against GM Gavrikov and he responded with a system involving g6, Bg7, c5, d6, Nc6 and e5. Please forgive me for not remembering the exact move order - this game was a few years ago.