The thing to do is make offers for shops that have lingered on the Job Board. A scheduler is probably not going to seriously consider assigning a newly-posted shop with a bonus, because it is the scheduler's job to get as many shops as possible done as cheaply as possible. Unless there is something unusual about the particular shop, a scheduler would probably want to let it sit on the Job Board to give other shoppers a chance to take it at the posted fee.
A hard-to-fill shop, regardless of the reason it is hard to fill, is the shop that the scheduler may consider digging down into their pocketbook and paying more for. If I am going to ask for a bonus, I usually e-mail or phone the scheduler with my offer before accepting the shop.; I figure if I accept the shop before asking for a bonus, I've already taken the shop "off the market" from other shoppers and I have already agreed to do the shop at the posted fee. It doesn't seem to me that the scheduler would have a motivation to give me a bonus if I had already accepted it. And, if I accept it first, and then the scheduler declines to give me a bonus, that leaves a problem. Do I complete the shop at the posted rate because I accepted it at that rate? Or do I cancel because I didn't get the bonus I asked for?
JMHO, accepting a shop at a posted amount, then asking for a bonus, and cancelling if the bonus is refused, would be a reason to give a flake citation if I were a scheduler. I think disclosing my financial requirements up front and coming to a fee agreement with the scheduler before accepting the shop is a professional way to handle it.