I'd bring a spare tube and a CO2 inflator; these are light and small, and you might even be able to fit a spare cartridge or two. Actual pumps are bulkier, and the smaller pumps without a hose tend to do a terrible job, particularly with the slightly more Presta valves you find on road bikes. (I'm assuming from "fitness bike" that you're talking about a road bike.)
You already have the saddle bag to carry all this in.
That multitool is pretty vital, so hang onto that. One that has a chain tool would be best.
You'll want a pair of tire levers to get the tire off the rim. There are some multitools that have these built into the tool housing, but I've not had luck with those.
It makes sense to bring along a patch kit in case you have more than one flat. Something else to boot the tire in case of a sidewall puncture can be handy. You can use a dollar bill or an energy bar wrapper for this, though. You can also bring duct tape wound around a stubby pencil for this: It takes up little room, and you've got duct tape with you. (A million household uses!)
Of course, as one of the commenters has pointed out, you'll want a water bottle and a bottle cage. How many bottles you bring depends on your mount. You can toss some energy bars in a jersey pocket as well.