I'm purposefully trying to avoid that ;p though bringing my own monitor is more or less the same I guess...
Sorry...I didn't read through enough to catch your budget or whether you sing or not (which can affect the effectiveness of certain possibilities) but got that a band IEM rig isn't in the cards.
One thing you might look into is the 3DME IEM system. It has app controllable ambient mics built into the ear buds (binaural set-up). I haven't used them, but if you search 3DME here, you'll find that a couple of members have posted about their experiences with them. I believe they're $800. So cost and actual effectiveness for you are concerns.
Another approach to consider is that you can be prepared for some different scenarios...like @Mike Caldwell, there is always the possibility that you can get a monitor feed. If they are running a powered wedge for you, there is very little effort involved in running that feed to your pedal board or wireless transmitter placed wherever they suggest. If you add a stereo headphone amp to your pedal board (e.g., Behringer P1), running in mono with two inputs, it acts as a two channel mixer...i.e., for your direct bass and monitor feed from the board. Running a wired setup like this, you could be prepared for less than $100 total depending on choices. With wireless, the consensus is that transmitters aren't a place to pinch pennies, so for a recommendable system, you're probably in the $700 and up range to put something together. If they're running passive wedges and/or are otherwise unwilling to work with you, you can't run that setup for that show. I'm not sure what it would take to run a mic instead of the monitor feed, but that could be fallback A. Here cost doesn't need to be a concern, but wireless gives some additional flexibility, and while having someone else run your IEM mix is sub-optimal when they are potentially doing a million other things, it can definitely be workable, especially where you have control of you bass in the final mix to your ears. You'll get the same amount of attention you would have gotten to wedge adjustments.
If you do look into a wired IEM system as a solution here, especially if you run your bass wired, I'd recommend checking out this video.