How to prevent protein precipitation?
Alas, the great problems with protein formulation. I assume that the labeling chemistry forces you to use the 8.5 pH. (I don't think this is necessarily true since succinimidyl chemistry does work at pH=7.2 and the NHS ester is fairly unstable above pH=8.6)

We usually tackle this problem entirely by brute force ie. testing multiple buffer condition with different bases and different salt concentrations. First attempt would be to try out all of the Good's Buffers notablely HEPES, TRIS, MOPS, Tricine, Maybe you should look at both zwitterionic buffers and non-zwitterionic buffers. In your case, the succinimidyl is vunerable to primary amines so avoid things like Tris/Glycine.

The second thing to test would be various salt concentrations. Since you're already dumping in Sodium Bicarb, NaCl should be great. Unfortunately, this is where things get tricky since it is hard to know if your protein precipitates at low salt or high. A test from 20 mM, 50 mM, 100 mM, 150 mM, 200 mM, 500 mM should cover most of the interesting regimes.

Alternatively the sudden change in the ionic environment around your protein may be causing it to precipitate. You probably should dialyze or purified your protein in PBS to allow it to refold appropriately.