You may want to change the bald tire. Also, it is good with clipless to practice in the park (so when you fall, it is on softer grass than the asphault / cement) where you speed up really fast and then slam on the breaks and see if you can clip out, so that you may be better prepared on the road.

The times I have seemed to fall have been when I stopped and for some reason the bike becomes unbalanced and because my foot is still cliped in, I go down.