@Kraig ******
the savings account part has no effect on if you can use their internet banking app, or not. The bank base that on your visa type, and if you have a work permit. Tourist visas have lots of problems getting approved for online banking. It is a separate company. Part of the anti-money laundering laws. Normal people do not go on vacation to another country, and open a bank account then leave a short time later, but keep the bank account active. Pretty much the only ones that get a checking account are businesses. Regular accounts are all just savings accounts, with a debit card. I have three different accounts with Bangkok Bank, including a foreign deposit account, that I keep dollars not converted into baht yet, and have online banking with all of them.
At the main Bangkok Bank branch on SiLom road, take the escalator to the second floor. Go in the first door on the right, and to the first desk. Tell them you'd like to open an account. It is the service section for foreigners. Lots don't know about it.
They usually ask you why. Depending on your age, you can tell them you want to start transfering cash over from whatever country you live in, so you can start getting the money needed to buy a condo if you are under 50, or to get the money transferred into a Thai account needed for your retirement visa because you are 50+, which is bt800,000. They might require some documents, but this usually works.