To Help strenghten the lower back I recommend an exercise called the stiff leg deadlift it can also be called a romanian deadlift. To do this you stand holding a pair of dumbells or a barbell at just below waist level, arms comfortably extended, and bend at the waist till the barbell or dumbells are around knee level. You legs should be slighly bent, but they dont move throughout the exercise. Do the exercise with light weight at first and see how you feel, I also recomend asking a trainer, or someone that knows this exercise to demonstrate it before doing it with a large amount of weight.
Here is a video demonstrating proper form.
http://www.uwlax.edu/strengthcenter/videos/exercisevideos/Db%20Stiff-Legged.mpg
good luck you seem like you are on the right track.
The discomfort you are experiencing is your body adjusting to being in the bicycling postion for so long, the exercise bikes seat probally is not helping, most are very uncomfortable. It will be better when you go outside and are distracted by scenery/having to stop at traffic crossings ect. Inside you can do a short burst/sprint (not all out, just a couple of seconds) out of the saddle every couple of minutes. A pair of cycling shorts will help, but it wont eleminate it. Riding a bicycle indoors is boring, and listing to music, watching tv or (if you can) reading a book helps. Changing your cadence also helps, do 5 mins slow, 1 min fast, then 10 mins at your comfort level (try to keep your exertion the same, go to a bigger gear (more resistance) for the slow sessions and a smaller gear (less resistance) for the faster sessions).
