CoinMama is a service that will let you buy bitcoin and ether with cash or debit card. Fees are relatively high (about 15% markup) but you will get your bitcoin (or ether) instantly.
With some debit cards you will need to undergo verification with selfie. The same goes for credit cards.
The payment executes via Simplex gateway. There will be no mention on the bank/ewallet side that you bought bitcoin. You can use a non-bank prepaid debit card linked to an ewallet.
Coinmama is available in most countries. If you live in the US Coinmama is only available in the following states: California, Colorado, Florida, Illinois, Indiana, Kansas, Massachusetts, Michigan, Montana, New Mexico, North Carolina, Pennsylvania, South Carolina, Tennessee, Texas.