Firstbuy,
1) Your deion of the events on this site, if found by the other guy, and could be proven to have come from you, may be used in court, if it goes that far. So be careful how much you talk about here.
2) You having just completed the physical left turn, but the butt of your car still inside the intersection -- that means anything happening at this time, strictly speaking, involves you taking the left turn. If the other guy was travelling straight, your left turn could be argued to have interfered his straight path.
3) The bike's excess speed definitely contributed to this accident -- being unable to keep reasonable control of his vehicle (bike) and stop in reasonable distance. Speed in excess of what the road condition allows.
Given 2 and 3, I agree w/ Single LaoMao this case can be argued as both parties at fault. It's then up to the insurance company how to take care of this. (Your car insurance, and the other guy's health/medical/car insurance -- depending if he owns a car and has an insurance policy.) Either: each insurance company paids the actual medical/repair bills of their insured; or add up total damages/bills, and split 50/50 - whatever.
If the policeman could remember what he was thinking at the time he was on the scene, it may even be possible the cyclist to be found "more at fault" than 50/50 -- based on that excess speed.
I'm not sure what you guys mean by "follow the flow of traffic". I am not aware of this law or regulation when going through driver's ed. This argument definitely does not stand up after one is issued a speeding ticket.
If there were no bicycle lane, then the bike was required by law to travel same as a vehicle -- this means behind other vehicles already in front of him, and on the right-side of the lane. If he's passing other vehicles on their right, at excess speed, that's also "reckless driving".
Most state's traffic laws forbids vehicles (that include bikes) to pass another vehicle (e.g. a car) who is stopped at an intersection for a pedestrian crossing the street. But I've never seen this law written as "...for a turning vehicle". So the oncoming cars stopped at the intersection for you to turn is probably irrelevant for this matter -- you're not a pedestrian crossing the street. Again, what is relevant, is that the bike's travelling at excess speed that was faster than the road condition allows.
4) If the cyclist is not happy with the settlement proposal from the insurance companies, and wants to sue, then he'll sue you. If it's determined by the court that you need to pay this guy for his stupidity - err... pain and suffering - then your insurance company will pickup the bill. *Possibly*, the sequence goes like: 1) auto insurance, 2) liability insurance (e.g. possibly part of your home insurance covers general liability), etc.
If it gets to this far, that means you have a lawyer already. Consult with your lawyer if you should sue the driver that signaled you to take the turn. I'm not suggesting this is morally correct; but you could consider it.