How do I write the deterministic rate equation for bimolecular reaction with similar particles?
There is really only one independent equation here because  

$\frac{dB}{dt} = -2\frac{dA}{dt}$

The "second equation" in the OP is just -2 times the first equation.  

Every molecule of A destroyed creates 2 molecules of B.

Every 2 molecules of B destroyed creates 1 molecule of A.