There are several online stores that use paypal (I use Paypal frequently). If you go to a particular website where you want to purchase, there should be a link showing what payment types they accept. I have not ordered from bike stores via Paypal yet so I can't say of any that accept it as payment method.

As well, if your debit card has a visa/mastercard logo on it, you can use it online to pay for items. Just enter the info the same as you would with an actual charge card, and its deducted from your checking account.