I also love to ride a bicycle maybe two or three times a week. It boosts my endurance and without adding any pounding to my legs, it makes my joints very happy. Sprints - there's not much of a substitute for those.
As far as your doubles action is concerned, I agree that the burst of movement toward the net can get tiring, but there are a few things to consider. My first thought is to offer that you can sometimes go to net behind your opponent's return, but that depends on the strength of that shot and how well you can handle it.
If your serve can force a weak return, then you want to get forward behind that shot and take over the net sooner than later. You'll control the action of more points that way. A weak returner may give you more short balls though, and those are relatively easy to transition behind. The thing is, you want to be able to approach effectively and that means having both a reliable slice and a decent half-volley. Those shots allow you to keep an opponent neutralized as you move forward.
Instead of crossing the entire distance of "no man's land" between your own serve and your opponent's return, these approach shots will keep you in business even as you move forward with less of a rush. Just don't stay back for too long after you serve with the idea of waiting for the best short ball to attack. That will leave you in the more vulnerable one-up, one-back formation for too long and the other guys will take the net before you get there.
In case you like to hit a hard serve, you should consider slowing it down a bit and serving with more spin. Your slower ball will still have an unpredictable bounce, which can force weak returns, but that slower serve will also leave you an extra fraction of a second to move forward before the return is on its way back. This can make a crucial difference toward successfully serve and volleying. Also, that serve should include enough of a forward drive that it's already launching you toward the net.
Oh, and there's also no crime in taking two or three extra seconds to recover between points. It's not stalling when you regroup before your next serve, but just don't get carried away. I know that some of these ideas are more tips that fitness pointers, but I think that both need some consideration when building a serve & volley game. Good hunting!
Running is indeed a good cardio workout, one every serous tennis player should to 3 days a week, however.....
For specific training, serve and volley, you need to replicate those movements. Moving forwards, lunging sideways, getting sideways and crabwalking back, done from a static position (your ready prep), is what is going to give you the first 3 steps after recogiition.
Go on a court, start at center baseline and replicate a serve, move to just inside the service line, then cover left, back to center, then right, alleys, then pretend you're chasing a deep lob back to the baseline.
Now from center position, go far left, back to center, then far right, back to center, and repeat the forward movement to inside your service line.
Do this non stop for 15 minutes, and you'll be gassed.
But this is EXACTLY the movements you need to play net.
For S&V exercising, try lots of quad work including one leg squats, weightlifter squats, and side lunges onto bosu balls. Lots of one leg balance lifting aids in the dynamic balance needed to volley well. Remember, bending those knees are the key to volleying well when moving up through low balls and half volleys.
As for S&V being dead, partially disagree. Not to be used every time but when an opponent is lofting balls back like Fed does with his backhand chip return, mix it up with S&V and get some easy points. Also throws off the returners rhythm. I find there are so few S&V today that many base-liners don't know how to adequately deal with a competent serve and solid volleys.
Keep at the S&V, another valuable tool in the tennis tool kit.