Two succint grammatically correct versions:
#1) I have a question and I figured you'd be the best person to ask.
#2) I have a question and I figured you'd be the best person to answer it.
In #1, you just ask (ie, you dont have to ask "it"). But this whole topic is fairly irregular, since we would also say Can I ask you a question? or Can I ask you something? (with a direct object). Of course, you might answer my question with: I don't know. Ask him.
In #2, it = "the question". The best person to answer wouldn't mean the best person to ask, it would mean the person who gave the best answer (of all the answers which were given).
#1 implies the person is better to ask, possibly for a quick simple answer. #2 implies the person is better to answer, perhaps because either a quick simple answer don't due, or they have special access to more current information. But this distinction is VERY subtle, and won't register with many readers, and is almost completely irrelevant in speech.
However, the best person to answer it could mean something different (although not in this context). For example: A call went out for volunteers, and, although not the first, he was the best to answer it.
Another example: I was asking a question, and didn't even get to the end of it... (think Jeopardy TV show). But the first person to answer, may not even have heard it all, and therefore may not answer it at all.