You just need to inform the bank from the very beginning about your plans, so it won't be any problem. They will ask where the money comes from and I believe you will need to provide some sort of proof! Other then that there is no problem to do so, even not with a bank in Cyprus.
Second the replies here. As long as you are honest to the bank they will not have any problems with your business! You will need a Certificate of Source of funds from a lawyer or similar.
That's actually a good idea. Most often they will ask you to make a detailed business description anyway so they can understand what you are doing and how your business actually works.