Accident with a car advise ?

You are not liable at all, make a note and act on EVERYTHING the above posters said.

Deal with everything formally as some(most?) insurers have a reputation for trying to drag things out to discourage you - do not fall for it, claim for ALL damage, injuries, any other consequences etc.

They will likely underestimate the value of your bicycle too.

Do not accept any cash offer from the driver (if they make it?).

Firstly, do NOT under any circumstances admit or even hint at admitting any liability at all.

My guess would be that the BMW driver is 100% liable as he pulled across lanes of traffic without checking correctly. He was maneuvering not you, but let a lawyer or cycling knowledgeable expert claims handler argue for you (which is why you need someone who understands).

Secondly, sit down and document everything as it is as fresh in your mind as you can. Was it reported to the police as RTCs involving injury need to be.

If you are a member of CTC, British Cycling, then speak to their insurance claims dept, or find a good lawyer who is at least aware of cycling, better still a specialist claims. Insurance companies are evil cold hearted bastards who will do and say anything to wriggle out of paying a penny, or better still getting the other side to cough up, so a very tough stance needs to be taken with them. If they found this thread, they'd use that to try and claim you admitting liability

Claim for time off work (if any, as your employer will probably want that to cover the wage bill of their injured employee). Claim for all you can and do not settle for the first offer. A good lawyer will help.

Note that filtering on a bike or motorcycle is specifically mentioned in the Highway Code and that other road users are warned to take care as a result. If you are overtaking on the inside, this is also allowed if traffic in the lane on your right has stopped moving.
Basically, it sounds like you were doing what is allowed and that the motorist did not take sufficient care when he cut across your path.
The degree to which the situation could have been mitigated by your riding more slowly and watching out for vehicles possibly crossing your path is what the insurance company will probably focus on. If you're a BC member you'll have access to a lawyer who will be au fait with the legal position regarding cycling. You could still contact BC even if you're not a member and ask for some advice.
The other points about CCTV from the bus company, taking photos and making notes of the costs to you from this incident are good ones and worth following.
The main thing is that you're not seriously hurt. Bikes can be fixed.

In my limited experience the insurer will try and mitigate their financial loss by putting a portion of blame for the accident on you, so you need to be prepared to defend your position.

Review the relevant sections of the highway code (cycle lane, undertaking, manoevering), go back and photograph the road, the lane (if he was pulling into a driveway perhaps he lives there and so should be aware of the lane), check for CCTV cameras, contact the operator of the bus say their cctv will have caught the accident and ask for the video from the bus' cctv.

Photograph your bike, your injuries (now & as bruising develops), damaged clothing and keep receipts of your out of pocket expenses (public transport, fuel, parking etc) and make a reasonable assessment of your total loss.

If it isn't worth pursuing then you are prepared if they contact you for his door, otherwise contact his insurer and say you will be making a claim and see what they say.

From what you have written it sounds like the BMW is trying to park parallel to the street. But I suspect that he actually was pulling off the road into a driveway. In the former situation I would definitely put the onus on him, but in the second it sounds like you may not have been taking due care. That's not a legal position, just IMO you should be wary filtering especially with buses because you can't see if they are stopping for traffic etc. which it sounds like what was happening.

Your first port of call sounds like it should be to an injury lawyer specialist if you are so inclined. They will assess the merits of it and then you will have a definite answer. From things I've read there are less meritous cases which have been taken up and succeeded (I'm not suggesting there is no merit to your case - I wasn't there, though I know I gave some of my opinion above).

The driver will be liable. They have pulled across the road to park against the flow of traffic and while this is in the do not category of the Highway Code it will go in your favour. As for the filtering, you were in a cycle lane passing stationary traffic so no offense committed by you. In fact I wouldn't be surprised that the bus driver has flashed the BMW through.

Take a note of repairs to your bike as well as loss of wages etc as you should be able to claim of the motorists insurance. Hope you heal up quickly and that your injuries are minor.