Heartbleed is not a real memory safety bug when program reads beyond allocated memory. It is more of improper reuse of previously allocated buffer and could exist in safe Rust just as well.
You're right, there isn't a classic simple buffer overrun that Rust would trivially catch, but you're missing two things:
1) The problem was really sending back uninitialised memory. In Rust you can't have uninitialised memory. The oversize allocated buffer would have to have initialisation data passed in (possibly zeroes)
2) You'd never write the Rust code like that anyway. The abstractions avaialble mean that you aren't separating the content of some data and the length to pass to allocators.
