is an online solution not possible without having to provide ID or credit card?
You might check localbitcoins, based on your location there are Bitcoin sellers. $20 is small amount so there could be sellers doing this without verification through bank account or other methods. Just check it out and expect to pay premium on localbitcoins, +20% probably compared to actual average price at exchanges, but maybe you find a lot of sellers so it could be more competetive.
I too suggest localbitcoin, it helps to find the traders with ease. It also helps with the trust mark. One can find a trusted trader and make his buying through localbitcoins as it has got the option to find traders of a exact location.