[git] Stashing only staged changes in git - is it possible?

Why don't you commit the change for a certain bug and create a patch from that commit and its predecessor?

# hackhackhack, fix two unrelated bugs
git add -p                   # add hunks of first bug
git commit -m 'fix bug #123' # create commit #1
git add -p                   # add hunks of second bug
git commit -m 'fix bug #321' # create commit #2

Then, to create the appropriate patches, use git format-patch:

git format-patch HEAD^^

This will create two files: 0001-fix-bug-123.patch and 0002-fix-bug-321.patch

Or you can create separate branches for each bug, so you can merge or rebase bug fixes individually, or even delete them, if they don't work out.