I'm getting a new fish tank in about a month (for birthday) because I'd love to get a Betta in a 5g to add to my tanks.

A friend of mine has a 5g they no longer want and are selling once they sell their fish this weekend. I asked if I could have their media in order to establish my new 5g. They have black gravel which I would love to have in my new 5g, so I'd like to just use all of their gravel. Is there anyway I can keep the BB alive in the gravel and filter until I can get my tank and transfer the media to my new tank to cycle it? Maybe just add a couple of fish flakes once a week to keep ammonia up? And do a
pwc maybe once every 2 weeks?
Also the filter is a Marineland Eclipse so the filter is laid flat which the water runs over and then goes through a biowheel. The tank I'm looking at getting has a Whisper 2-5 filter which is a vertical cartridge. Is there any way I can keep the BB on the filter alive and then somehow use the much larger media to cycle the new smaller one? Could I maybe cut the filter media out when I get my new tank and stuff it in front of the new?
Thanks!