Both of those mean 'to kill time'. 'Jikan' means time in general, and 'hima' often refers to free time and taking a day off.
(Fun fact: 'hima' could also imply quitting a job, being fired, or getting a divorce.)
By itself, the verb 'tsubusu' can be interpreted as 'to smash' or 'to crush'. Just as we say 'killing time', in Japanese you're clouting time over the head with a blunt instrument.
Not to be confused with 'tsubuyaku' (つぶやく), 'to mumble', which is now firmly in modern vernacular having come to mean 'to tweet/use Twitter'.
Mind you, that's also a great way to pass the time...
It's strange to me that I've never seen 'kill time' in English to be as oddly aggressive as 'hima wo tsubusu' is in Japanese. There are less frenetic ways to kill, after all. I could just casually slip some arsenic into time's coffee, instead of whacking it about with the percolator.
I think this is also because so much of Japanese conversation is passive. Like the idea that it's hard to directly say 'no'. And the concept of putting on a 'front' and not showing your true feelings publicly. It's hard to imagine suddenly hearing someone express the desire to crush their free time to pieces.
Why don't we go the whole hog?
時間を蹴っ飛ばす (jikan wo kettobasu) - to give time a good kicking - doesn't exist, but sometimes I really wish it did.