I've always worried about uship since you will always get the low ball shipper. Having good insurance on your bike is key too. Make sure you can buy something from the shipper and also if your bike insurance will also cover damage during shipping. That way you are covered for deductibles and extras.
You dont have to go with the lowest bidder. You can retain the right to select any of the shippers that place a bid based on which one you feel most comfortable with. Traditionally most people select the lowest bidder for the cost savings but I have seen instances where people are willing to pay a higher price for a more experienced shipper with higher service ratings.