Can you put what on your Verizon bill ? If you mean your billing method on an iTunes account then no.
Accepted methods of payment : http://support.apple.com/kb/HT5552
The available payment methods vary by country, but you can typically use these methods:
- Credit cards
- iTunes Cards
- iTunes Store gift certificates
- Content codes
- Store credit (including Allowance Account balances)
- ClickandBuy
- PayEase
- PayPal
You may be able to use other payment types in your country, like debit and Maestro cards.