Anita, I have the same issue with my Singer. With my machine dropped into the Gidget table, I can get to the front-loading bobbin, but not without a lot of difficulty. There simply isn't a lot of room to get your hand in there underneath to pull it out. You can't just raise the part the machine sits on (as Jennifer mentioned above); the mechanism isn't strong enough (it's not like those air-lifts in the more expensive tables). You have to pull the machine out of the opening and put it aside in order to raise that shelf.
I have my Singer sitting on top of the Gidget table, and don't generally use the shelf now. Primarily because of the bobbin hassle.