From this, I am assuming your item has bids at this time. To sell it to this person, you would answer their question with the buy it now price that you would accept, and then if you hear back from them that they want it for that price, you can cancel the other person's bids, end that listing, and relist the item to a buy it now price. The one downside to this is if someone else snaps up the buy it now before that person gets to it.
ETA: It is legitimate to end your listing early. Then to relist as the buy it now, eBay still gets their money. But by cancelling another bidder's bid, you do risk alienating them from your future listings. Also, if you do this, be very aware that you could possibly get more by leaving the listing as it is. Sometimes a buyer will ask for a buy it now to get a desirable item at a lower price then it may end up selling for.