Hey Jim!
I apply the 2% with my fingers. I just put about 4-5 drops in my right palm, and dip my middle and ring finger from my left hand in and rub it into my skin in circles. A little really goes a long way. Some people even use the 2% to only spot-treat, but I really like to use it for prevention on my entire face. The thinner you apply it (the more you spread each drop out), the faster it will absorb.
Applying it at night sounds like the right idea.

And, I think you will be very happy with the Alpha Hydrox Oil-Free Gel. I used that for years before I could no longer find it in stores, and tried the AH Enhanced Creme (which is also good, but just a bit heavier more moisturizing, which I don't need).
Good luck! Let us know how it works out for you! My face got a lot smoother and softer since I stopped using BPO as well, and started using PC BHAs instead!
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