Decided to have some fun with math on this one...
Assuming (completely unreasonably) that Perot's name suddenly disappears off the ballot, and that Perot voters split into not-voting/Bush/Clinton voters in the same proportions in each state...
The key state for Bush to win an electoral victory, then, is Iowa, putting him over the top with 274 electoral votes. If all Perot voters continue to vote, he needs to win 66.1% of remaining Perot voters nationwide to win Iowa. If 25% of Perot voters didn't vote, he'd need to win 71.4% of remaining Perot voters nationwide. If 68% or more Perot voters didn't vote, Bush couldn't win even if all the rest voted for him. (The formula, for anyone interested, is (c-b)/(2 * v * p) + 1/2, where c, b, and p are Clinton, Bush, and Perot's vote totals in Iowa, respectively, and v is the percent of Perot voters who still go to the polls).
Thus, it seems, from the polling data, that Bush still would have lost had Perot not been on the ballot. Whether Perot's presence in the campaign hurt Bush to a degree that caused his eventual loss--that can't be settled with numbers.
Just for kicks, here's a map (25% of Perot voters stay home, 71.4% of remaining Perot voters vote for Bush, handing Bush an electoral victory (274-264) by dint of the narrowest victory in Iowa (and a popular vote victory by about 500,000 votes / half a percent--Bush still under a majority of the vote, though).