Cycling, great sport, do it myself. I prefer the fat tire fitness side of life, but to each their pedaling preference.
To do it successfully at a recreational or competitive level requires a strong core, rock solid hip stability and quite frankly moving well off the the bike to ride your best on it. This is where the right approach in the gym (or wherever you like to strength train) is the key t pedaling stronger to ride longer.
Unfortunately, in spite of all the high quality information available (ANY Dan John book, James Wilson's MTB Strength Systems, The Girls Gone Strong movement, etc) there are still some "gaps" in what's recommended for bike riders and what actually works best.
Alright, with that being said, here are two exercises you should shelve, and two to put in their place.
1) Back Squats
Same idea here as the overhead press. Don't get me wrong, its a great exercise, when done correctly. However, there are several nuances to the movement that are critical to doing it right. Due to that, I feel it is best left on the shelf for cyclists.
You need quite a bit of core stability, thoracic spine mobility and hip stability to back squat correctly. Plus quite a bit of ankle mobility at the bottom of the squat to keep the load in the hips and out of the knees. Historically, this is another area cyclists are notoriously deficient in.
Again, four very common areas for cyclists to leak stability, power and strength. Plus, shoulder mobility affects bar placement quite a bit, so if you've got range of motion issues there, do yourself a favor and keep a bar off of your back.
What to do instead
Since you produce all of your power and force one leg at a time when you ride, do it in the gym as well. For this I like loaded lateral lunges.
This will involve the core, low back stabilizers, grip strength, the lats, hips and legs, or, very thing that locks you in place uphill. Not only do you get the benefit of the above mentioned, but you will be moving your lower body left and right to open up hips against the repetitive stress of only moving the legs up and down in one range of motion while riding.
2) Seated Rows
Again, sit all day at work, sit when you ride, so why sit to lift? Especially since cycling involves pulling the bars away from the ground out of the saddle with one arm in a rotational stabilization pattern through the trunk.
Even if you add in a single arm variation of this movement, you're still sitting down.
What to do instead
The split stance single arm row is a much better option. It will work everything you need to ride a bike successfully:
Single arm pulling
Single leg hip stability
Trunk strength you need to keep the back happy uphill
Rotational core stability (remember, it's better to have strength in the muscles that prevent rotation rather than the ones that make it happen)
Mid back strength to keep your spine as straight as possible seated
Grip strength (your foundation for driving upper body power production out of the saddle)
Make sure you crush the grip (particularly in the pinky) to get the most out of the movement.
Hope this helps simplify your training off the bike so you can have a lot more fun when you're on it. As always, a HUGE thank you to Alison Corcoran from Goldilocks Training for the video content help!
Hope this helps, thanks for reading!