The no hassle approach would be to just buy a new lock core and key (51252303682) for about $25 and a new lock housing (51162303024) for about $23 and then modify the new lock core to work with your ignition key before installing it.
Taking your old lock in to a locksmith is a gamble. If he is not used to working on BMW locks, you get to pay for his learning curve. Also, he may not have the correct parts, so they have to be ordered. Recently, I was quoted $50 to swap keys in a padlock and I had the keys! Fifty bucks for job that takes less than ten minutes and I bring the work to him. Man, I am in the wrong job field.
If you feel that you must DYI, there is tons of info on the web to help you. Many locks use round pins inside but your lock uses flat pieces instead.
If I remember they are called wafers. If you are lucky, your old parts can just be moved around in the lock to match the key used for your bike.
IBMWR's website is a great place to start reading, but there are many more websites to help you. READ ALL OF THEM before you tear into your lock.
Also, make sure that you read the websites about Neiman keys also. They are the OEM supplier for BMW.
I have to agree with Frankenduck on this one. Less hassle to buy new core with keys and then make the modifications. If you buy the new lock and housing from your local dealer, they may change the key over for you at no charge. It is a simple job and your dealer will have the parts