DA40 pilot reported while attempting to land after an unstable approach; the aircraft bounced several times prior to the pilot executing a go-around.

Narrative

Initially I came in to land. I did not have a squared off base and looking back I think my airspeed was too high. Since I was focusing on trying to descend I did not line myself up appropriately with the runway. I touched down and began bringing yolk to chest to assist in braking/ slowing down. (I think I began to bring the yolk to my chest but looking back I think I had too much airspeed. In an attempt to make a taxi way I think I applied too much back pressure and essentially had enough speed to take off like i did.)Instead of continuing to another touch down; the aircraft made almost a short field take off and proceeded to bounce 3-4 times on the runway. After the third or fourth strike I applied full throttle and began my climb out/ go around. Should have had a more rectangular pattern.Should've chair flown more prior.Should've recognized the unstable approach sooner and went around while on final.Should have recognized the unstable landing prior to first touchdown and went around sooner.Should not have been so focused on trying to make a taxi way.