Why not let the drivers see the destination and price and then make the choice if they want to accept it? When we are at it the customer should be able to increase the price to encourage drivers.
I see it this way: drivers reject giving a reason, one of the two: too cheap or other. Then the customer gets information about how many drivers rejected because of the amount and they get an option to increase it.
As it is I often feel bad about requesting short trips. I feel most drivers don't want them and the situation is uncomfortable for everyone. I would like to have an option to pay enough so it's worthwhile for them to take a short ride.