Transferring money from one country to another is an important thing which is responsible for the growth of International Trade or to put it this way, the growth of International Trade has contributed a great deal to the increase in money transfer requirements and needs from the part of people.
You can transfer money through your bank as almost every bank has such a facility available and if you are transferring the same currency to and fro then it would be easier and a lot more cost effective than if there was some form of a currency exchange involved.
If you would like to do your money transfer from europe then you will want to consider the amount of money that you may be transferring as you may be able to do your money transfer for free if you make use of certain services that can offer you such a facility.
Banks are definitely the safest option for you however they may in hardly be the cheapest option or even the quickest option available to you as they may take a while to complete your funds transfer especially so if you are transferring bigger amounts of money. This would again obviously depend upon the bank that you may using as different banks may have different policies with some being cheaper and faster than others.