I'm with Stu--go with the Nonlinear Lev-Mar Fit. The helpful aspect for you is that the default fit equation hardwired into its "Target Fnc & Deriv Nonlin" subVI is actually the very function you're trying to fit:
y = a0*exp(a1*x) + a2
Here, a2 is the offset you're asking about. If you simply wire your X and Y value arrays into the Lev-Mar inputs and provide an Initial Guess Coefficients input of [1,1,0], you'll probably get a decent result for data that crosses close to zero.
Regards,
John Lum
National instruments