Try using the $0.56/mile rate as a start. Then consider if you want to request distance pay for your time to drive (what about $0.25/mile?). See if you'll even break even with what they're offering. Another strategy to consider is seeing what shops are along the way and if you can somehow make it a profitable route. If you see other shops along the way, you can see about asking for bonuses on those as well.
In the end, you have to ask yourself what would it take to make the shop worth it for you. Is reward, whether it's the reimbursement, pay, etc., enough for you to take it? What kind of profit are you trying to achieve out of this?
In the end, it doesn't hurt to ask, unless you believe it'll be assigned to someone else before your inquiry even gets looked at.
Shopping the Greater Denver Area, Colorado Springs and in-between in Colorado. 33 year old male and willing to travel!