have never bear hunted, but you can have my opinion anyways
#1.. as long as you alone chased it up the tree, or if it just was up a tree and you found it, or your in the tree and see it coming up your tree or another tree ..... Yes it's ethical
however going to a ranch or game farm and having assistance from other people or dogs to chase it up a tree.... No ( paying your money and picking out your buck or any animal and all your doing is pulling the trigger or string, isn't hunting or ethical in my opinion )( the exception is hunts for those that have special needs )
#2 aim for the vitals, if it's up a tree ...
your on the ground, you should have a quartering away shot
if your in another tree, you should have a broadside shot
if he's coming up your tree, forget ethical... it's him or you