Both Guns Blazing Reload

Do you have to reload each time you attack with BGB or only when you would normally make a reload check?

I assumed the "Make one Reload Check for both of your guns, one reload reloads both of them." Portion was just saying to treat them as one weapon.

You are correct. The reload check for both weapons is a bonus feature of the BGB schticks, you do not have to reload your weapons any more frequently than you would otherwise.