I've just purchased CAS via BTC coins. What I did is - I just went to bitcoin.com and purchased it online via VISA Virtuon card ( you will have to provide your info along with payment and an image of your ID or passport ) and then used that BTC to purchase CAS coin on their website.
Make sure to not purchase CAS amount that is less than 30$ total ( it is listed in their FAQ ), so use BTC amount that comes to at least 30$ when converted.
About your bank question: yes, I believe that you would just fill in a request to send the money from your own bank account to their bank account ( or use mobile banking via mobile app of your bank if you have one ). Also, if you are doing it this way, remember that the bonuses they are giving on the coins purchased will be affected by the day the money actually arrives to their bank account and not the day that you've actually sent it. So BTC or ETH transfer in order to buy CAS would be the fastest and most valuable way to go here ( because of the large coin bonus that you get if you buy it sooner rather than later ).
Hope I've helped!