I've done two things in the past:
1. Baby powder - it dried the area better than a moisture-rich deodorant and I could reapply without clumping.
2. Face wash my underarms in the shower - I use a few different face washes (for price or just to change it up), washes with astringent or exfoliators (sp?). What they did for me was get the icky oils out of my skin and helped cleanse my pores to minimize the bumps. I was also applying baby powder in substitute for deodorant.
Basically, I cleaned and dried out the underarm area and was able to keep applying baby powder if I sweated it off during the day. Just kept a small, vacation-sized container in my purse and reapplied in the bathroom. I have naturally dark hair and pale skin, so I'll always have the darker color in my underarms, but I no longer get the bumps.
I'm certainly not a doctor, but this worked for me. Good luck, and hope it helps