What you are talking about is a payment gateway that works with Vbulletin.
A merchant solution or merchant account is simply a specific type of bank account that allows credit card or debit payments to be authorized, the gateway does the work via program integration.
If you are in the US as your tag signifies, you can get a merchant account very cheaply and easily then choose a gateway that integrates with the software you desire
if you have any questions about merchant solutions feel free to hit me up, its what I do ; )