In short, very safe!
Security is one of our top priorities and one of the areas where we feel a lot of merchants and existing payment processors are lacking.
We make every effort to ensure the security of your details provided to us, and will continue to increase the security of the service we offer through the effective use of technology.
With regards to bank details specifically, you are not required to give us your banking details unless you need to receive a payout. Most users who pay for things online will probably never need to furnish their bank details, it's really only the receivers of money (Premier and Business account holders) who will need to do this.