Originally Posted by Russ Roth

From dealing with other people, if you're already in decent shape you can probably go out and ride 2-3 hours and cover 30-40 miles. If you're in really good shape I don't doubt that you can go out and cover more like 40-50 miles in closer to 2.5-4 hours. I've met plenty of healthy people for whom this was easily the case. What people lose sight of that requires strength training is the level of fatigue that starts to set in after that, in decent shape the first 20 miles go by nicely, the next ten are more tiring and the legs start feeling dead at 30 particularly when you haven't learned to pace yourself. Same with being in really good shape, 30 miles isn't a lot but by 50 the arms are getting tired, the but is getting sore and your legs aren't used to churning out the miles as the mind starts to wonder when it will be over.
This is why people are recommending miles on the bike and looking at a shorter distance if available. Your legs aren't used to the long term sustained effort that you're going to ask of them, you're talking about 130 miles, assuming rolling terrain your average if good, and you're not a racer from what I can read with real experience, will be 15mph at the upper end giving you a good 9.5 hours of riding if this is a one day ride, don't be surprised by 12mph average and closer to 11 hours of riding. Stops will be added in and required for drinks, snacks, and bio-breaks and add to the weariness of getting back on the bike. That's a lot of hours training your muscles to just function and the gym won't help that much, it'll make you stronger but you need endurance.
Personally I would try to get out for 25 mile rides 3 days a week for the first week and try to do 40 miles on the weekend in a single ride. Use it to see how you feel and how you recover. The second week I'd try for 3 30 mile rides and a 60 mile ride on the weekend. 3rd week try for 35 mile rides 3x and go for a 75 mile ride, see what recovery feels like. Week 4 stick with the 35 miles and maybe see if 40 is doable, and try for 90 miles on the weekend. Final week do a couple of 40 mile days and nothing for 3 days till the ride. I'm not a trainer but this is what I would try to do, more than that would be hard to schedule and pushing harder is liable to hurt you. If you can't do the final 90 mile ride you have no chance on 130, if you can make it but suffer you'll possibly make 130 but expect to suffer more and if you can easily do it you'll ace 130mi. A month though isn't the best time frame but good luck.