Regarding pick up: That's your choice entirely, you can agree for the customer to pick up if you wish, but if you didn't include pick up as an option in your listing, you can of course refuse if you don't want to let them.
Regarding the bidding: Not quite sure if you actually mean a best offer bid or not. If you are talking about someone making you a best offer below what you will accept, you have the options there to make a counter offer or just reject their offer altogether.
If we are talking about a normal bid that someone has made on your item in the course of an auction, well that's not an issue while the auction is running, of course bidding is part of it.
If an auction has closed and the winning bid was below what you anticipated getting, then unfortunately you are obligated to sell the item at the winning amount.