Two pronouns in one sentence

Solution 1:

Unfortunately, in this case the sentence is ambiguous. There is no way to determine who that "he" is referring to without further context. I would assume that it is the blogger because Bob is called out by name in the following sentence, but even this is not necessarily correct.

Solution 2:

I think there's a subtle clue that "he" probably refers to the blogger. "if he could" usually means asking for permission, and Bob doesn't need permission from himself to do something.

If the blogger were suggesting that Bob do the giveaway himself, it would be more idiomatic to write "if he would" rather than "if he could".

This isn't completely unambiguous, though, because "if he could" can also be used to ask if someone is able to do something, and in that case it could still refer to Bob's ability. But I think this would be an unusual thing to say, so I think my earlier interpretation is most likely.