The way you describe it "bouncing around" makes me think that the thread is catching on something. If it were a regular bobbin in a bobbin case, I'd suggest you check to make sure the bobbin case is still round - sometimes if you drop it, it will get a tiny bit out of round, not enough so you'd notice, but enough that it makes a difference. But since it's a drop-in bobbin, I don't know what to tell you, other than to second what Annette said.
Regarding the bouncing table... even "sturdy" tables can sometimes bounce a tiny bit. I found that when I moved my machine so that it wasn't directly in the center of the table, but rather sitting on top of one of the legs to my right, it didn't bounce.