Put a bottle jack under the low spot. Hook a chain at the top edge of one side of the bucket, run it under the jack and hook to the top edge of the other side.
Go slightly past straight, as it will spring back.
Or turn the bucket upside down and rig it like this:
If you have a rose bud, and oxygen & acetylene torch you could try to heat shrink it. I would go with Xfaxman suggestion of the bottle jack and chain first! Sometimes buckets are so reinforced. Only force will fix them.
Indeed these buckets are usually very hard to bend, so you may have to cut and weld as I did. Even my 20T jack
was not forceful enough to bend without cutting.
I bent the middle of my 83" Cat bucket.. I was pissed... but a friend of mine used his Cat 330 excavator to push it back to straight by flipping the bucket over on 4x4s and pusshing down in the middle with his bucket. Worked great ant took about 1 minute.
330 size excavator! I bet it bent it back.:laughing:
Iirc my 4 in1 had a cutting edge on the back of the (moving) "clam". It looks like your's does also (the bolts in your pic). I'd remove that before you try to bend it back. It may have an arc to it and bend the clam back as far as you can then try to bolt the c/e back on with the arc reversed.
There is an excellent article on heat shrink repair for structural members......and i even posted a link on my Facebook page years ago.....but I can't seem to find it in my downloads.
If the bottle jack and chain doesn't work. Wrap a heavy chain all the way around the middle of the bucket with the bucket closed. Once the chain is on slowly open the clam shell. As the clam shell swings open it will bend the clam shell back into position. Use a long 4x4 along the top and bottom of the bucket back to spread the load and not bend the bucket back. Cut a section of steel pipe and place it over the front cutting edge so it won't cut the chain.
I easily bent the front clam shell back into position on my CAT backhoe using this method.