I'd say your script displays ads in reverse chronological order (i.e. - newest ads first) this is the norm.
If so, its just a matter of writing a custom "bump" script where the user provides the username and password and possibly the id of the ad they want to bump. If the credentials are correct the user is prompted for payment details. Upon payment success, the payment processor triggers your script to update the ad in the database with the current timestamp.
You'd possibly want to modify your database for this. It's always a good idea to keep the original timestamp of when the ad was erm, added, just add a timestamp field for "bump" which by default gets set with the current timestamp when the user initially adds their ad. Then just modify your php script to sort listings by this "bump" field.