I never had problems with bumps and ingrown hairs until I started waxing, and then it was horrible for almost a year. Now it's almost back to normal. Almost.
For me, there's a series of things i find super important. I always use a fresh sharp flexible razor. I always exfoliate the areas I shave regularly, and areas prone to ingrown hairs I exfoliate with a gentle facial scrub with a low dose of salicylic acid in it. While shaving, I like prepping with aveeno oatmeal bars which are super moisturizing and lovely. I use them when shaving my legs too. After the shave, I use a cetaphil antibacterial bar and then a gentle moisturizer when I get out.
The whole series helps make sure your skin is clean and soft and the exfoliation helps prevent the hair from getting trapped just under the skin. The salicylic acid also helps draw out any infection there might be plus any hairs that would be otherwise tempted to curl back under.
Hope that helps!