Same thinking here...... Spent just over £2k on a bike. It not only paid for itself in the first year but saved an additional ~£700 on a ~£3k worth of travelcard.
I strongly suspect the explosion in the number of people cycling to work here in London is due to the criminal cost of (so called) public transport. Also worth factoring in is that after a year the bike still has a value unlike the Oystercard.
When we lived in London, we found it was cheaper to buy a 110cc scooter on finance than it was for my wife to buy a monthly zone 6-2 pass for her oyster. I think with the finance payment, petrol, and insurance, it came to less than £90/month as opposed to the nearly £150/month train ticket.
But onto the subject at hand. I don't really obsess over the cost of cycling. It's still cheaper than my car, takes roughly the same amount of time, and is a much more pleasant journey.