Got the Swim and Run down, now the bike?

Ok, as the tile says it is time to play cycle catch up. My swimming is solid; I am just doing some maintenance works outs. My running is almost to a half, I could hold a descent pace for 10 miles. Now I need to get in the saddle and move. What cautions should I take? Is it like running and lesser part swimming? I know running ramping up the distance too quick can be bad, swimming for isn’t a huge issue. The longest riding I have on a bike is ~45-50 mins. I did so indoor spinning over the winter, at the gym. And just got a new bike and took it out for the first time this weekend.

My goal is to get out 3-4 times a week; I would like to get comfortable with ~20 Mph. I can mix in some very challenging terrain too. Starting next week I will be running, 5K-10K in the morning, before work. Cycling to work would be ~15-20 miles of city travel, which I would not prefer to do, but might give it a whirl. So I wouldn’t rule it completely out of the question, but very impractical. I have a section in mind, that is ~7 miles, virtually all uphill one way, then down. Would it be an option for some climbing / interval work? I also have another that’s ~12% grade change, and a very steep valley.

Any suggestions to get my base up while building stamina and holding a good speed. I am a poor cyclist, and now have the time and focus to address it.