I go to the gym on a regular basis and do a fair bit of running. I feel like I'm fit enough to do this. It would be a one-off ride from Wembley to Slough and back so it would be a fair bit of road which could be a problem.
As a one-off, that should be completely doable. Your fitness from running and the gym should be plenty enough, especially as the route is pretty flat. Bear in mind that it will be tiring, since cycling uses different muscles to running, and the saddle may get a bit uncomfortable if you're not used to it. Make sure you have plenty of water and something like a cereal bar or a banana to eat half-way would be good, too. (You want something that will release energy over time, rather than a big sugar hit.)
Riding in traffic can be mentally tiring when you're not used to it so definitely consider a route using quieter roads and cycle paths, even if that adds a few miles. The thing you want to avoid most is narrow roads with lots of traffic: if cars can overtake you easily, everybody's much happier.
And there's lots of public transport available so, if you get to Slough and can't bear the thought of cycling home again, you can always get on a train, though don't try to do that at rush-hour.
Man, just do it! There isn't much that can go wrong. If you feel tired, turn around midway. Take a mobile phone with you in case something happens, look up the weather forecast, take something to eat and drink with you (or some money to buy some). If you end up at a different location than initially planned, so be it; my personal experience is that too much planning destroys much of the fun of riding. I often start thinking about going for an hour ride and end up doing 100km. Or vice versa.
As an inexperienced rider you may do 10 mph (16km/h), thus 3 and a half hours of riding time for 34 miles (54km). So just make sure you don't start in the evening.
Nope - go for it. Here are two suggested routes from Strava, which were generated at https://www.strava.com/routes/new and then clicking a start and end point, and changing some options.
This first one is based on "most popular with cyclists" and runs for 30 km with total elevation change of 204 metres.
Another choice is "minimise elevation change" which saves you 5km and 50 metres of vertical ascent, but is a less popular path with cyclists. I see part of it appears to be down the A40 motorway, but there appears to be a cycle path there.
Finally if you'd rather make your own way, here's the "heatmap" for the area. You can access this at http://labs.strava.com/heatmap/#13/-0.44289/51.51782/blue/bike
Our LBS has a Saturday morning ride for which we often get beginners. Many are no longer young and not particularly fit. They can do 17 miles of flat ride before lunch. I wouldn't worry about the amount of exercise if you have a nice break in the middle. Discomfort after that much riding is more of a worry. Allow enough time, about two hours each way with rest stops. You will probably ride faster than that, but don't push too hard. The main thing is to have fun so you keep riding.
I typically tell people that any normal healthy novice can get on a bicycle and do 10 miles per hour without difficulty, so if you can walk for two hours stop for lunch and walk back, then you can do this with less work. Pack water, a cellphone and lunch money. If things go wrong you can put the bike in the boot of a cab.
If you were a little older I'd say work up to it over a month or so, doing progressively longer rides to give your body time to adjust and tell you how it's doing, but at 17 you can recover from almost anything. Have a great time.
I can't tell how much you've ridden already, but maybe (if you're not tubeless) practice changing a flat in the field to make sure you have everything with you that you need. Ride a mile from the house then pretend you have a flat, then change or patch the tube right there by the side of the road.
It's do-able. We have some guests, a couple in their 20s or 30s, who both know how to cycle but aren't accustomed to it. They were able to go somewhere and back, 25 km each way.
- It took them several hours; partly because they stopped when they got there. But also because they cycle relatively slowly.
- They borrowed my bikes which are "hybrids" of reasonable quality (several hundred euros with good tires)
- They went along a semi-paved river tow-path which is closed to vehicle traffic, so no worries about that.
When they went again some weeks later, they found it easier. It seems to me too that any route is easier the second time you do it.