I think I would have to order one, do you think the bladder tank I've got in now would be ok to leave running for a week or 2? Would putting a bladerless one back in requiring any special priming or prep?Sure you can just put a bladderless tank back in. Sounds like the bleeder is working fine. So, you would need to reinstall a check valve with a Schrader on the inlet, and an AVC or Air Volume Control on the side of the tank. You can get galvanized like Quicktank, or fiberglass with an AVC on top.
You may not have noticed any smell because you are still injecting air in the lines? Plug the bleeder and the smell may come back. Is iron orr sulfur common in your area? Ask the local well company.