I can think of three bands that had guys both responsible for keyboards AND bass in their respective bands: Ray Manzerak for the Doors, John Paul Jones for Led Zeppelin and Mike Mills for R.E.M. I know that Manzarek played the bass parts with his feet, but what about John Paul Jones and Mike Mills for the songs that needed both keyboard and bass parts? How did they do it?
Too late to edit: it just came to my mind that Rush’s Geddy Lee is also a contender for this thread, and he even was also the lead singer! I don’t know Rush’s work very well, but I include him in my inquiry.
I don’t know about the others, but Geddy had a foot controller (as did Alex for a while), though I’m sure he sometimes played keys with the bass on the keyboard for that part of the song.
Jones and, I believe, Lee used bass pedals on stage.
Geddy is Canadian. If you asked, he’d probably come to your house to demonstrate, pick up the tab for the expense, be Sorry for being late and Thank You for the invite.
Hey, he’d have to take a transcontinental flight for that, but as long as it’s on him, I’d love to be a given a private concert in my living room. 
(maybe he can invite Ray Manzarek, John Paul Jones and Mike Mills for the event. THAT would be a jam session!)
This guy still blows my mind.
One of the treats of having our church services online (besides FF’ing through the boring parts) has been to watch the organist’s feet. Separate video inset during his (very ambitious) postludes at the end of the service. Dude is rocking those pedals, sometimes too quick to notice all the riffs he’s doing.
First discovered this listening to Lee Michaels back in the day. His live album was just organ and drums and I asked “But who’s playing bass?”.
That’s what usually gets used in these cases.
We’ve had at least two dopers (well, one doper and one doper’s aunt randomly bump into him. Your description sounds pretty accurate.
R.E.M. just brought along hired help. Scott McCaughey from The Young Fresh Fellows and Ken Stringfellow from The Posies, for instance, both spent long stretches working with the band.
17 years ago I asked a similar question about Eddie Van Halen, who plays both lead guitar and keys on Van Halen’s studio recordings. Here was Dr.Righteous’ response:
The man (literally) behind the curtain for VH live is the keyboard player from Night Ranger Alan Fitzgerald.
Jack Blades, singer/bass player for NR, speaks about it here: