This was addressed in B5: Racing Mars. In short, they have some supplies and financial reserves, sufficient to allow them to set up alternative supply routes. They also mention growing food in the garden that runs along the centre of Green and Blue Sector.
Sheridan: I've been going over these reports trying to figure out how we're going to get along with all our supply shipments from Earth
cut off by the embargo.
We've got two, maybe three months of reserves. Then we are going to run out of things. Small things at first, then more important things.
Something breaks, we may not be able to fix it. And you can forget the
spare parts for the fighters.
Ivanova: We can go black market if we have to.
Ultimately they blackmail the various smugglers who operate out of B5 into bringing in food and medicine from Earth-controlled space.
Ivanova: Instead of the usual destructive crap you guys bring in I want you to start transporting useful things. Those food items
that we can't grow here, medicines we can't fabricate spare parts for
fighters and shuttles and other ships.
In B5: Thirdspace they set up an additional line of supply to Earth space via Interplanetary Expeditions.
Sheridan: Thanks to the blockade, we're running short of supplies around here. Spare parts, certain foods we can't grow...
Trent: And you want us to break the blockade and bring you whatever supplies you need.
Sheridan: If you're going to work here, you may as well bring lunch. I'm just trying to make sure you bring enough for
Finance-wise, there's a big push to become financially self-sufficient, largely by encouraging free trade and charging ships for docking and repair.
Sheridan: It'll take a long time to get the level of trade back to where it was before we broke away from Earth. Right now, we need the docking
fees more than ever, but we can't catch a break.
In the same episode, the various non-aligned worlds sign the Babylon Treaty, aimed at improving the station's accessibility (and safety) as a neutral port. There may have been some element of financial transfer involved.