I have tried a lot of different things for shaving. And a lot of the things that worked for other people were hit or miss with me. But here is what I have found works the best:
I use a razor that I only use for that area and only use it twice max for that area. The duller the razor is, the more likely to get the little bumps/razor burn. Unfortunately for me, the razor is too dull by the third use. To extend the life of it and make it not so wasteful, I will then use that razor to shave my legs and under my arms at least a few times after I stop using it for my pubic area. Those areas do not really get razor burn for me, so it being slightly dull (and I mean very slightly, like I do not notice the difference in those areas) does not matter.
I try to sit in a tub of warm/hot water for a couple minutes at least before I shave and also shave with a thicker cream type lotion or a body butter. I tried the conditioner, special gels and stuff, exfoliating first, etc.
I only shave over each area a maximum of two times. I learned that if you keep shaving over it to try and get it smoother, it ends up causing the bumps every time.
If the hair is long enough that I can trim some of it, I do that first. Since I only shave my pubic area completely during a certain time of year, or at least not all year, some of the hair tends to be to curly point and I find it clogs my razor less if I trim it first.
I think that pretty much sums up what I do. Hopefully some of that works for you. Those little bumps are not fun at all!