This question is simply answered directly, but when you dig a bit, you find that the question is more complex in reality. Although complex, not confusing, so let's get started sorting this issue out.
Bed bugs can't actually burrow into memory foam because the cells are too tight and constricted for them to actually live in the foam. Instead, they do the same as other mattresses, they live in the bedding, tufts and over places they can hide from the light.
These little creatures detest light just as we detest these parasites. They cause painful and itchy wounds as they attack as you sleep, sipping on your blood like most parasites, but they can't live in memory foam.
There are many articles on how to remove them from your bed. However, that does not cure the problem of the initial infestation. Removing them from the bed is one thing, but they can still be in your home. Most have issues ridding themselves of bed bugs in general, but there is a post I found that is very blunt on how to get rid of bed bugs once and for all. You can read that interesting post on how to get rid of them naturally, without chemical or poisons here: http://luxuryofthepharaohs.com/bed-bugs-memory-foam/.
There are always solutions for problems, but once you understand the dynamics of the situation, finding that solution becomes much easier to identify and implement, bringing you the peace you need. And after dealing with bed bugs, you need some peace.