Huh? Have ever actually paid a bill without using a computer? It doesn't work like you describe at all (unless you live in a really rural area or you're deliberately trying to make it difficult for yourself). Here's how it works:
1. Get a bill in the mail.
2. Open it, and write a check for the amount.
3. Put the check in the envelope, stick a stamp on that, and then put it all in your home's mailbox.
4. The mailman comes and picks it up, and it goes where it needs to go.
No buses, no trips to the post office required.