
IMHO complaining because he can't feel the bass is absurd.
Ideally the sound should be processed and balanced for different locations and users. I usually worked with a full PA that included separate monitors for each band member. My amp served as my personal monitor and if anyone wanted more bass, they asked for it to be adjusted in their monitor mix. Sometimes the audio tech told them no, because there was already way too much bass coming off the stage.
If your rig is pushing the room, the priority should be on adjusting your bass amp to balance out in the house. Creating the best mix for the audience is likely to degrade the balance on stage. The bass may be too loud for some, and not loud enough for others. There can be some reasonable concessions to give a decent balance on stage as well, but it's not really realistic to expect optimal sound everywhere.
If the keyboard player can't hear you, then a solution may be to change how the band is set up, so he can be closer to your amp.
This can still pose problems because each person has different needs and expectations. If the keyboard player moves his amp closer to you, it may result in too much keys at your listening position. I.E. there will be no way for both of you to get the mix you want, because each of you have different needs.
Pro musicians tend to understand that the sound is rarely perfect...it may not even be close. However, you don't need perfect sound to do the job, and anyone who has to have perfect sound should probably stay home and play along with recordings.
IMHO, if the keyboardist wants to feel the bass, then it should be on him to buy the necessary gear. He will need to coordinate with you to make sure the gear will work with your rig.
He could get something like an Eich BassBoard.
The BassBoard is a tactile transducer. When you feed it audio, the platform shakes. It's not totally silent, but you are unlikely to hear it over a typical bar band's stage mix.
The BassBoard is not self-powered. The keyboardist will also need some sort of an amp to drive it, so the keyboardist can adjust the intensity of the shaking. If it's not clear, this option represents a significant financial outlay. So, IMHO the chance that the keyboardist will do anything except continue to complain is unlikely.
I think communication is the first step. Try to resolve the situation with diplomacy. Some people can tolerate whining and some cannot. If it's stressing you out, then either figure out how to prevent the comments from bothering you, or figure out how to stop them.
Stopping the comments could involve securing the keyboardist cooperation or it could involve you leaving the band. If the situation get's too toxic, weigh the benefits of staying VS quitting the band. If you do decide to quit, then put in notice and try to avoid burning bridges.
If you decide to ignore the comments, make your intentions known and put down some boundaries to let the keyboard know that you intend to disregard future complaint on the matter and it's on him to work out a solution. If he chooses to escalate the level of abuse, at some point you may need to give everyone an ultimatum, either the keyboardist puts a cork in it, or one of you must leave the band. Just make sure you understand, it could be you or it could be him, and the choice is likely beyond your control.
I suggest weighing the pros and cons. How important is it for you to have this sort of musical outlet? How likely is it that you can find another opportunity that is better? The reality is most bands seem to have an abundance of dysfunctional interpersonal BS. So what are you getting from being in a band that justifies dealing with the resulting stress?