I have been on Wellbutrin for a good number of years and never had acne as a side effect. I have had adult acne (not as blown-out an affair as how badly adolescents get it), yet I never had acne as a teenager, so it is possible to have acne for the first time as an adult.
The benzoyl peroxide is in the over-the-counter acne treatments (they contain either that or salicylic acid). You would see it listed on the product as the active ingredient. You have to be careful, though, as it can be extremely drying to those with normal skin (not really oily). I think it is difficult not to overdo it w/the benzoyl peroxide. I would start with the salicylic acid first. Johnson and Johnson's makes a line of skin care called "Clean and Clear"--cleansers, treatment, even oil-free moisturizers--all with the salicylic acid in it.
If you have the $, you may have seen the "Proactive" acne treatment advertised on TV or magazines. It really, really works. I used it, my sister uses it, I have heard of a lot of people being happy with it. It is pricey, though, $50 for a 1 month supply, but I found the treatments lasted much longer than using them for just 30 days. They put you on "autoship" to receive the product every 30 days, but you can tell them you don't want to be on autoship and then you just order it as needed.