I love dyeing with bark - it often holds a lot of color, it reacts well to modifiers, and it does not require a mordant. Tree barks have a higher degree of substantivity than leaves or flowers, which means the colorant in bark naturally bonds with cellulose fibers at a molecular level without the help of a mordant (though a mordant can improve color up-take). Black walnut hulls, indigo, and lichens are also substansive dyes - there is a great explanation over here. Because I most often dye linen and paper, I have come to really appreciate the affinity between bark and cellulose fibers.
Tree barks for natural dyeing: oak elm ash alder birch hawthorn cherry and other prunus species apple pear elderberry walnut willow
Bark should never be stripped from the trunk of a live tree, it causes too much harm to the tree. However, twigs can be cut from live trees following the rule of taking one-tenth or less, spread over a large area of the plant. To expose the dye-rich inner bark, the twigs can be shaved down using a paring knife. This always seems to me about as fun as peeling asparagus, so when I use twigs I simply chop them into small pieces using garden shears.
It is an easy matter to gather twigs or branches from cultivated plants at pruning time. Apple, plum, pear, cherry, apricot, and elderberry barks all give beautiful colors. If you have orchard trees or a friendly local orchard owner, remember to save the prunings for up to year.
Another method of collection is to simply wait for a windfall and gather fresh fallen branches after a storm has passed. Some diseased trees such as elms suffering from Dutch elm disease will drop whole branches, even without the help of a gale.
Of course the best way to gather ample quantities of bark is to keep a woodstove. I am not exactly the lumberjack-type, but the man in my life takes pride in heating the house with wood. The wood comes from diseased or damaged trees on the property that need to come down, or occasionally a tree that will be used for furniture making. This gives me heaps of bark that can be dried and saved! Twigs can be prepared as described above, or swathes of bark can be taken off using a spokeshave. Take both the outer bark and the spongier, softer inner bark. Pictured above is a spokeshave and its effect on a cherry stump. Anything you are not using immediately can be spread out in a breezy place until thoroughly dry and stored in paper bags for up to a year.
Another benefit of the woodstove is a place to keep the dye pot simmering for hours during the cold months without using the energy of the kitchen stove. It is also useful for making wood ash lye, a pH control and modifier. Rather than purchase soda ash or ammonia, you can fill a plastic bucket 1/3 with cold wood ashes and top with cold water. Leave it for about a week until the ashes settle out and the liquid feels slimy. Decant the wood ash lye into a glass jar without disturbing the sediment, and it can be kept indefinitely. A 1705 dyer's treatise on right proper lye making and the merits of various ashes can be found here.