I suggest you try the bootstrap prefix in Stata and its options. This allows bootstrapping for most Stata commands. Here's an example for linear regresion:
Looking at it again, DEA hasn't been programmed too well, so the estimates aren't immediately available to bootstrap. Relatively easy to tweak the DEA code to leave the efficiency scores around in e(b), then they could be picked up by bootstrap. But if you're new to Stata, you'd need to learn how to do this first.