Are you using any type of icing or ganache under your fondant?
yes I do it is a butter-cream recipe i got from cake supplies plus using high ratio shortening
With buttercream make sure you are not putting too much on. Just a thin coat works for me, then I let that crust a bit, I lay a smooth paper towel on the buttercream and smooth it with a spatula. You can use a smooth paper towel or wax paper. Then I lay my fondant.
I used to get bumps too and it was because I was using too thick of a layer of buttercream and I wasn't smoothing it well enough before laying the fondant.
I have used a variety of cakes and they don't seem to be the cause of lumps.
I do have my go to recipes posted on my blog, they all work wonderfully under fondant.
Hope this helps
Your cake design is beautiful!