Can I pick the bonus item when buying an uncommon item at the entrance?
What bonus item?
Do you mean if Monterey Jack purchases a Unique Item while Waiting at the Entrance (i.e. Buy a Souvenir), does he obtain 2 Unique Items for the price of one?
Yes. his Special Ability (Whenever Monterey gains 1 or more Unique Items after setup, he receives 1 extra Unique Item) applies when he buys a souvenir.
The same applies to Dexter Drake (for Spells), Bob Jenkins (for Common Items) and for my unofficial version of Rex Murphy (for Clue tokens).