I've spent quite the amount of time looking for a way to remote control a Chromebook and have yet to find one (I'm also a Pixel + Chromebook user). What I do with my stationary bike / trainer is put the laptop on a stand (basically one of these - though they make many different heights/shapes/sizes to different use cases - https://www.amazon.com/SHW-Height-Adjustable-Mobile-Rolling/dp/B09JQ6J4L7) That way the laptop sits right by the bike while I work out, within easy reach.

The other thing you could do is look into a small 2.4ghz or Bluetooth air mouse or even a keyboard w/ trackpad combo (very inexpensive) and use it to control the Chromebook over a distance (I've used this with a Chromebook - it just uses a small USB-A dongle - and it's very easy to use over a distance - https://www.amazon.com/Logitech-Wireless-Keyboard-Touchpad-PC-connected/dp/B014EUQOGK).