I had surgery May 20th this year. I was riding my mtb (on the road) 4 weeks after surgery. Just a short 30 minute ride. I did this every other day. I chose my mtb because of the comfort compaired with my road bike.
One week later I rode the bike for 45 minutes. Ofcourse my sternum was not completely healed at that time, but I rode my mtb on flat tarmac roads. Sometimes, on small bumps I could feel my sternum, but never a big deal.
I must say that I have had a mini AVR and the scar is only 3 inches long. There is a picture of it somewhere here in one of the topics.
After 7 weeks post-op I started with my road bike for 1 hour rides. At that time the sternum did not give me any problems at all.
8 weeks 1.5 hour ride, etcetera.
I am now 4 months post-op and 3+ hours on the bike is no problem.
I sometimes feel my sternum area, but that is most of the time the breast muscles that are causing this.
Please listen to your body and do not overdo it.