Do you have an automatic rejection amount? Maybe their amount minus the BPF is under the rejection amount? What does it show for them if they view the listing; and likewise what does it show for you?
Or you could ask them to watch your item and you send them an offer - it would go anyone who was watching or had viewed the item (and hadn't had an offer*). In that case someone else could buy if first at that amount.
(*) It's likely more complicated than that.
