Depends upon the bike and depends upon how you want to do it.
Attaching a bunch of arcade/fighting board switches to the handlebars and then cannibalising a controller to wire those into the relevant buttons (be it the actual buttons or debug points within the controller) is easy enough. All those things people do to make rapid fire controllers, adapt controllers to USB, controllers for disabled people/young kids wanting to play with parents and controls to automatically play games are what you will be doing here.
https://learn.adafruit.com/usb-snes-gamepad/overview for a general idea -- for all the advances in controllers over the decades they are still switches and analogue sensors and you can replicate that. Theoretically you could mechanical linkages to press buttons but... don't use mechanical linkages, and some kind of solenoid is not going to be much better.
Using pedals might be harder. Two main choices depending upon the bike
If it is your utterly basic resistance band on a wheel deal then you will have to add stuff to sense the motion, and this might also be easier for the second case.
If you have one that spits out some data to a display on the screen then you might be able to tap into that in either the display part (they tend to be rather custom data so might be more annoying, especially if you are asking this sort of question) or tap the sensor part -- I imagine most use hall effect sensors and a magnet on the wheel these days (if it sees 1 pulse it knows the wheel has rotated once assuming there is the one magnet, better designs will be more magnets) but you might still find a dynamo one wherein a dynamo (basically a motor in reverse) taps off the wheel in some form to spin and generate a voltage. A dynamo will generate a voltage, and reverse it when going backwards, depending upon the speed you go so you can use that to make minimums or turbo boosts as necessary. Either way you feed the data into something like a teensy++ or arduino which can do things like calculate speeds and choose to press the accelerator only when you are pedalling fast enough or detect you are going backwards and make sure to press whatever combo is necessary to reverse.
You can buy hall effect kits for things these days but a cheapo bike pedometer might also have enough gear and wires already to do things, if you are good it might also have a data out you can play with but I will skip that one for now.
I would say you will want the teensy/arduino stuff in there as it will also allow you to adapt it for a little old lady or dude with calf muscles looking like they kick down trees for a living.
You say leaning is not a thing for yours. OK but I will note you can always put the bike on something that does lean (you could probably do it with a few load cells and two sheets of decent ply* or metal if you wanted -- a standard human + bike makes for a fairly decent load at the size of the average sheet of ply while still not likely to tip things over) and much like the pedals you can tap that off to calculate relevant controls. I don't know how much Tony Hawk ride controllers go for these days but they might be able to scavenge something if load cells are not your thing, as might a wii remote, but you will likely be programming something more serious in those cases and figuring out how to make it work.
*weld or bolt two H shapes out of angle iron or box tube, two bearing surfaces in the middle at each end so they pivot (nothing drastic -- a gate hinge set might even do), at least two load cells (one for either side, probably four or maybe 6), some stops or springs to prevent things from getting too out of hand (though load cells themselves can take quite a bit if you want them to) and you have your tilt setup.
Depending upon how much money you want to spend on this I would consider doing a prototype board first. Just something basic like tap off all the points on the controller and make a quasi fighting game/arcade board with some kind of spinner (be it arcade, or two plates with a rod in the middle with your HE sensor you drive with a drill) to simulate the wheel before adapting that. Arcade switches if they come in a form you want are also quite nice as they tend to be somewhat shielded where a basic bag o bits is going to get shorted the first time someone drips sweat onto the thing.
It should be no great hassle to wire up three or so sets of switches for each button for people to either grip the crossbar or the vertical bits, though you might want to figure out a dominant one for the turning controls.
I will note though that most games are built for controllers and if you thought racing wheels detracted from top scores then this will be worse, especially if you are going in for the leaning thing. Not so bad for human against human but AI is a whole other thing.
