If spacedock is a hub of local travel than she very likely has antimatter to fill up the tanks of those in need.
I see no reason why there couldn't be a antimatter creation crew aboard. It's a rather big station, definately a metropolis in orbit. Why shouldn't this metropolis make enough antimatter for local Earth traffic? Why not have the local traffic hub be able to take care of ceeating the fuel for the local traffic? Naturally, if you want to supply the solar system with antimatter you'll make a station within the orbit of Mercury and collect mass solar energy for your project. But, as someone said, fusion energy is cheap in Star Trek and making antimatter is way easier then than now. I like the notion of spacedock maker its own fuel, even if it's only for the locals.
Finally, even in TMP they're doing some pretty amazing stuff with force fields. It seems perfectly possible that the inside is a place where a ship berths to be surrounded by a force field that can then be pressurized. And even that is assuming that the whole place isn't pressurized and the forcefields are at or near the doors so that the bay doors can open without depressurization...just like shuttlecraft. No, we don't see it. But we don't see it anywhere in TMP movies (that I remember) and yet I assume it's true for them.