I'm not a runner, but I play ice hockey. It totally depends on you and your delivery experience. Go with your gut. There's no need to wait until 6 weeks - there's nothing magical about that number. For some people, it's 2-3 weeks, for others it's 2-3 months.
If I were you, I'd start with light exercising now if you feel up to it... swimming, walking, etc for a few days and if it feels fine, then start running. If you had stitches, you might be extra sore down there and may want to hold off on the bike - or even running since it can add pressure. If you feel fine after a few days, then continue.
After my 1st was born, I was so tired and sore I didn't think about exercise for the first 2 months. At 6 weeks, it still hurt to walk, let alone run or skate (I had a big tear with lots of stitches - heck, I didn't move the hospital bed after delivery for 3 days except to use the bathroom!).
After my 3rd was born, I walked easily to my postpartum room an hour after delivery. I was back at ice hockey practice 2 weeks after she was born and played in a hockey tournament at 6 weeks. My doctor said it was OK. I skated at hockey practice with her blessing until I was 5 months pregant (had to quit when too big for the gear!). She understood that I was in good shape, a really good skater (20+ years now of playing ice hockey!) and I'm on a nationally ranked ice hockey team.
Every delivery is different, every person is different so you are the only one who can make that decision. Start slow and stop if something feels wrong or painful. Keep going if it feels fine. Many studies have shown that the sooner new moms get back to their old routines, including exercising, the better relaxed they are and are much more likely to not develop depression.