Bush might have been able to win if he didn't have to spread his campaign thin against two separate opponents. By concentrating on fighting Clinton alone he could have probably run an effective campaign.
Furthermore, Ross Perot stirred up anti-establishment sentiment, similar to how Trump is. Given that GHW Bush had spent nearly 30 years in politics and was the incumbent, he was viewed as the embodiment of the establishment.
(1) Bush was trailing Clinton in the polls *before* Perot re-entered the race. So the difficulty of attacking two opponents at once was evidently not the source of Bush's problems.
(2) As for the argument that Perot stirred up anti-Bush sentiment and thus softened Bush up for Clinton,
"The basic problem with assessments like this is that they place far too much weight on campaign messaging, tactics and events — and not nearly enough on the basic structural factors that dictate the outcomes of most presidential elections.
"When it comes to analyzing ’92, by far the most important thing to remember is that the race featured an incumbent president (whose party had controlled the White House for an unusually long 12 years), rising unemployment, and sagging public confidence. After spiking to an artificially stratospheric 91 percent after the winter ’91 Gulf War, Bush’s popularity steadily eroding as the bad economic news mounted. By Labor Day, his approval rating had fallen under 60 percent. By Christmas, it was under 50 percent. By March of 1992, it was nearing 40 percent — a dangerously low level that generally signals looming defeat for an incumbent. In fact, by early March, polls found Bush losing to both of the Democrats’ top two prospects — Bill Clinton and Paul Tsongas.
"All of this happened without Perot and his big ears and charts in the picture. It wasn’t until February 20 — two days after the New Hampshire primary, in which Bush was humiliated by Pat Buchanan’s surprisingly string showing — that Perot, then largely unknown to most Americans, announced on “Larry King Live” that he’d be willing to run if volunteers put him on the ballot on all 50 states. The Perot movement quickly gained steam and climbed to impressive heights in national polling. By late May, he was leading the three-way horse race, slightly ahead of Bush and far ahead of Clinton.
"It’s not a mystery what was going on: Voters had already given up on Bush..."
http://www.salon.com/2011/04/04/third_party_myth_easterbrook/