a bottom filter? Do you mean an undergravel filter? They were quite popular a number of years ago; but seem to have fallen out of favor. While they do work; they really require a complete tank tear down every so often so you can physically remove the muck that accumulates under there.
So no you dont "need" an undergravel filter. You can choose whatever method of filtration fits your tank, your needs, your budget, your desires, etc. Yes if you set it up with a filter out of an established tank it will cycle faster.....sometimes instantly. As far as how long you'll have to wait to add fish there really is no uniform answer. It depends on your tank and doing water tests will determine whether or not your cycled. I'm not a fan of trying to cycle a tank with fish in it; so my answer would be you'll have to wait until you're cycled! could be instant if you use a filter from an established setup; or it could take weeks -months
