If you used a backwards loop cast on, try doing the long tail, instead. The rule of thumb for how much yarn to allow for in the tail, is about an inch for each stitch you're going to cast on if the needles are a medium size (maybe US size 4 - 10) and a 1/2" per st if smaller needles, and 1.5" if larger.
As for the bind off-- that's a common problem. Just do it very, very loosely. You can see how it's going as you bind off, so if it's too tight, rip it back and start it again. Try using much larger needles than the ones you used for the scarf, that can help.