Short and well-known term for "jump from one branch to another"

Solution 1:

The bird flitted about in a strange wood.

Solution 2:

Birds flit from branch to branch.

to move lightly and swiftly; fly, dart, or skim along

Apes brachiate.

Brachiation (from "brachium", Latin for "arm") is a form of arboreal locomotion in which primates swing from tree limb to tree limb using only their arms.

"I tried to brachiate through the trees like Tarzan, but I ended up breaking my arm instead."

Solution 3:

I can't think of a single term meaning “jump from branch to branch”. The closest I can get is to offer a somewhat more specific alternative to jump: hop.

hop
(of a bird or other animal) move by jumping with two or all feet at once: a blackbird was hopping around in the sun

If the bird is not jumping on feet, but instead flying around, I would go with flutter:

flutter
(of a bird or other winged creature) fly unsteadily or hover by flapping the wings quickly and lightly

^{(New Oxford American Dictionary)}