Agree with the above.
Especially with running, injury history matters. Do you have bad knees, shins, back, etc? Even seasoned runners seem to commonly miss chunks of time, and going from 0 to pretty serious has additional risks. To avoid injury, you want to increase training volume slowly. To reach an ambitious goal, you want to get at it immediately. Those things work against each other. As UG mentioned, being heavy doesn't help matters. Maybe focusing on base while losing weight early would help?
I could give you some decent advice on how to do this cycling, but running is different. For that amount of money, I'd probably hire a trainer. The problem is, the training market is as bad or worse than the poker coaching market -- if you're not an expert, how do you even know the person you get isn't full of it?
As a cyclist, 6 minutes seems short. NFS's idea about interval training seems spot on. You need some base to put that intensity on top of. Most of the folks I know who run do hill intervals, but they're all maniacs. Skinny people who do trail running and qualify for Boston might not be a good guide for milers.
Quote:
few days later booked a bet where I have to run 6 minute treadmill mile by June 1st.
Is this limited to one official attempt, or can you try as many times as you want until you succeed or run out of time?