How can I buy online without a bank account?

Ask the retailer if you can mail a money order. If you’re in the US, the post office has very low fees for money orders. I recently needed one for $300. My bank asked for a $5 fee, the post office charged $1.20.

Get a PayPal account. Then use the MokeyPak card system to add money to PayPal. This way you don’t have to use a bank account or credit/debit card to back the PayPal account.

@Afos22 I second @wildpotato‘s vote for PayPal. I have several bank accounts but do a great deal of my shopping using my PayPal account. I have a PayPal Mastercard debit card that I can use online or in local shopping. When I use it as a credit card, I get 1% of the purchase credited back to my account. I save several thousand dollars per year by doing that.

See if anyone can sell you bitcoins for cash near your community. Then you can either pay for a lot of services with bitcoin, or get a temporary credit card loaded via bitcoins.

In any case check and read these:
http://www.weusecoins.com/

https://en.bitcoin.it/wiki/Trade