Tough to know for sure based on your description, but a couple possibilities:
1) Float height not correct or float sinking. Don't remember the spec off the top of my head but the Rochester was my first rebuild, knowing less than nothing, and it was easy to do. Have a shop manual that can help you through it?
Float buoyancy can be checked by submerging it in very hot water and looking for bubbles.
2) Carb castings warped to the point you're seeping fuel. Possibly in combination with one of the conditions in #1. The fact that it runs OK might suggest the warping is relatively minor.
There are a few other possibilities as well, but these give you a place to start. There are some very easy to understand rebuild videos on YouTube and if you buy a kit from a reputable source....the rebuild could not be any easier.
Fiddling with the float height cured my leak. But your may or may not be so simple. The B has issues. Many will suggest you replace it with a Carter but might as well try some simple things first.
