Ray, I would be wary of heating that fabric. TPU varies a lot, and some compositions are for heat-sealing and some aren't. Even if the TPU on that fabric would work for heat-sealing, it would only seal to another TPU with a similar composition and a similar softening/tack temperature range. It wouldn't bond to a dissimilar TPU or any other material. I've tried that.
If you try to use heat, it is more likely that the coating on the bucket will peel off and your bucket will no longer hold water. If you want to bond something to that fabric, I would recommend urethane glue.