I wouldn't be embarrassed - it's not like cleaning around a BAHA abuttment is common knowledge!!
Anyway, it seems all doctors recommend different ways of cleaning your abuttment - mine had me clean with a soft toothbrush right from the very beginning. I know other doctors say not to do that. I had a problem with infections around mine because I think I was being a little overzealous with the toothbrush (my dentist tells me the same thing) and that would probably cause little scratches that would let germs in. Now, I use it about once a week and just remember to be a little more gentle. I used antibacterial soap for a while, but now that I haven't had any problems (knock on wood) I just use shampoo. I also have a handheld shower head, so I can aim the water right at the abuttment and make sure all the soap is rinsed off and it's nice and squeaky clean.
The first year, I also had an issue with the skin wanting to grow over the abuttment, which would make it easier to become irritated....leading to infection....I have a steroid cream called Clobetasol that I can put on now if I notice it getting puffy. I put a little on at night and by the morning it's fine.
I know it sounds like a lot of work, but after the first year with mine, it's really low maintenance. So, I don't think I actually answered your question, but you should probably check with your doctor to see if he's a fan of the toothbrush or not. Good luck!