Reload/refit option at port or at milk-cows is instantaneous and uses no game time; returning to port is two weeks as already mentioned (though this value can and has been modded; check the mod forum).
If you're using the OHII campaign mod (and if not, why not?

), then you don't need to return to port to 'request' a mission in order to complete it - sinking the correct ships in the correct area of operation will still count towards a mission that has appeared while at sea. I assume the same would be true of the stock campaign, but since I've never actually played an un-modded campaign I can't say for certain

If no mission is available, free patrol & sink what you like until the next one appears (mission availability dates are now available in the main OHII thread, courtesy of Trevally).
Returning to port updates the crew experience total so you can 'upgrade' your sonar operator etc, and is the only way to alter your weapon/equipment loadout - but beyond that, there's no reason you can't stay at sea and just refit/refuel when you begin to run low