The way we introduce new dogs is to bring the new dogs into the house with our dog off the lead and then drop their lead too; it’s always resulted in a positive relationship. It depends on the temperaments of the dogs though, if you've never noticed any aggression from your Staffy you should be fine especially as the English Bull Terrier is a pup your Staffy won't see it as a threat.

There's no reason they should fight long term if they are trained and exercised properly.