So legally, I've found the following:

First, (and I just discovered this), the branches on Bob's property
are actually not owned by Bob... If it were a fruit tree, and it bore
fruit, Bob would not be entitled to the fruit. Therefore it is
actually Dan's tree, and those are Dan's branches. (This is Canadian
Law, which seems to be consistent with US Law). It seems that Bob has
the legal right to trim the overhanging branches so long as he does
not unduly damage the tree. But, just to muddle things, if Bob does
trim it, Dan still owns the trimmings. This means that Dan would be
responsible for disposal. Next, Dan does not have the legal right to
enter Bob's property to do any trimming without Bob's consent (and the
trimming would obviously need to be done from there). If a branch
were to break from the tree and damage Bob's property, Dan would not
be liable (unless Dan did something to aid the branch in breaking, or
he knew the state of the tree on his side of the property line might
result in damage to the neighbors property ).

There would be other special cases if the tree was planted after Bob
moved in, but those don't apply here.

Those of course, those are all legalities. At this point, the tree is
in good condition, so no breakage is likely. Bob is insisting that
Dan trim the tree and pay 100% of the bill (which, given there's a
pool involved, is not insignificant), but Dan doesn't feel this is
appropriate, and doesn't want to pay (and of course, he's not legally
obligated to, so for now nothing's happening).