Algodoo

As far as I can tell, there are only two ways to prevent it from slipping out of the grip: either use notches or a movable floor to put something under it, or use wheels to constantly pull it up.

I also though of notches, but they would only work once the bucket is in the air - so that's complicated because I can't get under the bucket.

I also thought of the movable floor, but it would be big and complex - still seems the most realistic option. Gives another problem though: how to drop the water without the bucket?

Wheels - I tried, but they didn't seem to have enough grip with grip 2.0. Might be able to tweak that, but it's complex.

Anyway, all those are strange ways to improve grip. It's obvious that grip 2.0 is not at all comparable to, say, using your real life hand to pick up a glass. That's at least ten times more grip. It's still a challenge to pick up a relatively slippery bucket, but has less to do with transport.