I think Bush would actually have a chance at a 2nd term in this scenario. Clinton, at times was third in a three man race before Perot withdrew, it wasn't until after Perot exited that Clinton took the lead and when Perot re entered, it was Clinton, not Bush, that took the hit in the polls.
Yes, and Bush's campaign actually celebrated it at the time, stating that it was what they needed to draw even with Clinton. And yet after they lost conservatives immediately concocted the lie that Bush only lost because of Perot. This was still being echoed decades later by trash like Ann Coulter and James Carville's wife (I don't respect her enough to look up her name).