Hi there.
As to whether your biking performance is likely to improve, that is certainly possible. It depends on many variables, including how much your narrowed valve is impeding your performance now. My aortic valve narrowing was similar to what you are describing- going down to .87cm2 just before surgery and now, with my new mechancal valve, it is over 2cm2, per my echo last week.
@pellicle linked two threads in which I document my recovery and some of my fitness training. From those threads you will see that my fitness has returned over the course of months and I now can go at it pretty hard again.
Today I hiked my favorite local mountain again for the 10th time in the past 3 weeks. I hiked it a lot in the year leading up to my surgery- about 5x per week and, although I can't claim that I am climbing it any faster now, I do feel as fit now as I did then, and go up the mountain, a 1,200 ft elevation gain, without any difficulty once again. It is much easier now than it was 2-3 months after surgery. Keep in mind that I was not experiencing any symptoms prior to surgery, and I was flying up the mountain at a fast pace back then, so it is not as though I am now setting world records, but I am very pleased that I am comfortably able to challenge myself and climb at a similar pace as I did prior to surgery.
Many members report an immediate difference in their cardio- but those are typically folks who are very symptomatic- out of breath climbing a flight of stairs for example. It does not sound as if you are that symptomatic at this point and it is hard to know without more information whether the larger valve area will translate into immediate results. But, if your narrowed valve is slowing you down, once you have recovered from surgery and slowly return to physical activity with your cardiologist's guidance, you very likely will experience a higher performance level with enough training.
It sounds like you are eager to test yourself with your new valve, that is fine and good, but really important not to push too hard too soon. Follow the guidelines of your medical team in how hard you train. It is not worth risking a paravalvular leak just to see if you can beat your previous athletic performance too soon. Most physicians give the green light for return to vigorous cardio training after about 3 months. I waited 4 months before I really pushed myself, even though physically I felt as if I could have done so a lot sooner.
Personally, I have found recovery and the return to fitness very rewarding and I hope you do as well. Don't be discouraged if it takes a few months longer than you anticipated to get to the fitness level that you want. With such a narrowed valve it is very likely that there was an invisible ceiling on your performance, so in time and with training, you have a good possibility of improving on your previous level.