how do i get them out of the bucket without tearing the roots?
Here is a reply to the same basic question I wrote some time in the past. Rather than type it all again even though some wording might not seem to totally fit what you said the repotting information is still valid.
Below the original portion is some additional information about what can be done if you have plants sharing a container and have tangled roots and a person wants to separate them.
Oh .. you want to know about transplanting.
 
Ok, well if like most people you began your seedlings in a plastic cup or some small container you soon found that you have to repot into something larger because the plant’s roots are running out of room to grow in.
 
The below soil mass/area/size of a plant is very nearly always close to being equal in size to the above soil mass/area/size of the plant. Because they take such different shapes it is hard at times to imagine that being the case but it is.
 
Once roots begin to circle a pot the plant is under some degree of stress. The longer the circling is allowed to continue the worse the stress the plant is under becomes. Among some of the problems root-bound plants can have are stunted growth, stretching, smaller and slower bud production, needs often watering, is easy to burn even if using low percentage nutrient solutions and wilting.
For future reference .. when you repot follow the following steps.
 
Select the pot size you will be transplanting into. (I suggest growing in nothing smaller than 5-gallon pots and I normally use 7-gallon pots and I start out my plants in them and never repot.)
 
Allow the soil in the pot your plant is in to dry out and slightly pull away from the sides of the pot.
 
(The following applies if you are right handed. If not reverse the hand position/use instructions)
 
Partially fill your new larger pot with quality soil so when you insert your plant into the new pot and fill in around the rootball the top of the soil will be at the correct level.
 
Pick up your old pot with your left hand.
 
Place your right hand on top of the soil with the main stem between your first and second fingers.
 
Gently tap the edge of the pot on a countertop or a workbench or something similar. The entire rootball should slide out in one piece, possibly with a slight amount of soil loss, but no damage to or loss of roots unless the plant was so root-bound that the roots had grown through the drain holes. If that is the case if you use plastic pots cut the pots so the roots can slide through. If you are using clay pots and you do not want to damage them then clip the roots instead, but saving them is always best if possible.
 
Your plant and rootball are then securely held in your right hand. Inspect the rootball and if it is tightly packed/twisted/root-bound slightly score/cut the edges of the rootball and also slightly score/cut the bottom of the rootball.
If you do not score/cut the root-ball that the roots will want to continue to follow their circling pattern and their growth progression both down and to the sides into the fresh deeper soil will be much slower. Each cut root will push out new roots and they will go both out and down into the new soil.
 
Place the plant into the new pot.
 
If the surface level of the old rootball is to low or two high remove some soil or add additional soil.
 
Next fill in around the edges between the rootball and the sides of the larger pot.
 
Water thoroughly to cause the soil to settle without compressing it too much by packing it down by hand. If needed add additional soil and water again.
 
Normally plants will undergo very little to no shock when transplanted in this manner but it would not be an injudicious thing to do to use a product like SuperThrive or something with the same general properties because they will reduce plant stress helping them to overcome it quicker and easier.
Additional to the below to fit the individual question better:
Tangled roots - Bare root transplanting:
Remove plant/rootball from pot as per above.
Use a hose or repeatedly dip into bucket of water, a hose is better, removing all soil from your plant's roots.
Gently separate the roots of the different plants and of course separate plants.
Partially fill new larger pot with soil.
Hold plant with roots dangling into the new pot. Gently add soil so you do not tear the fine roots.
Attempt to spread out the roots in layers if possible spread them out as much as you can, again being gentle.
When filled with soil water heavily to settle soil without pressing down compressing it. Doing that will tear roots.
Allow to dry thoroughly.
Again, SuperThrive or some other similar product that helps plants overcome stress is not a bad idea. If a bare root transplant is done correctly plants should undergo little to no stress or shock at all but it is not a bad idea to take the belt and suspender route in such cases.