They didn't get a second three-peat until they signed Rodman. Some people say that was the decisive factor that tipped the scales towards the Bulls.
Pick up after 1993 season...
1993-94: Bulls still had the likes of Pippen (top 5 player), Grant (stud PF), Armstrong, Cartwright, and added the likes of Kerr, Kukoc and Myers. If Jordan is there they're the most dominant side in the league, and probably a 65-70 win season. The East Finals would probably have pitted Chicago vs New York (again) and I doubt the Knicks would have won out. However, facing a solid Houston side could have pushed Chicago to seven games as Olajuwon would have toyed with Chicago's big men. That said, if the Knicks were up 3-1 on Houston, I fancy the Bulls would have closed the Rockets in five or six games.
Prediction: Bulls four-peat
Depth chart:
http://www.basketball-reference.com/teams/CHI/1994.html
PG - Armstrong, Kerr, Paxson
SG - Jordan, Myers [no trade for English (not necessary)]
SF - Pippen, Kukoc, Johnson (also 3rd SG)
PF - Grant, Williams, Blount
C - Cartwright, King, Wennington, Perdue [King traded for Longley in Feb 94]
1994-95: Grant jumped ship to Orlando, Cartwright with Seattle, Williams with Philadelphia, Paxson retired, Johnson released. Brought in Harper, Buechler, Krystkowiak, and Foster, drafted Simpkins. Jordan and Pippen were still top 5 players in the league but losing Grant, Cartwright and Williams and replacing with Foster and Krystkowiak, and ultimately starting Kukoc at PF, showed a massive downgrade. Meanwhile, the likes of Indiana and Orlando (Grant) strengthened and the Knicks were still a solid side as well. I would say this Bulls side would still be a solid bet to win 58-64 games with Jordan for a full season. However, a second round matchup with the Knicks would be physical per normal, and in the conference finals the upstart youth of Orlando versus Chicago's experience and tiredness (basically five seasons played in past four years with playoffs). Shaq and Grant dominate Chicago's soft front court and lack of rebounding efficiency, while Hardaway destroys Armstrong/Kerr duo and Anderson proves himself a decent defender (he actually was) in attempting to contain Jordan (as much as possible). The Bulls would exact their revenge in 1996.
Prediction: Bulls lose in East Finals to Orlando, 4-2
Depth chart:
http://www.basketball-reference.com/leagues/NBA_1995.html
PG: Armstrong, Kerr
SG: Jordan, Harper, Myers
SF: Pippen, Kukoc, Buechler
PF: Krystkowiak, Foster, Blount, Simpkins [Waived Foster Dec 94]
C: Perdue, Wennington, Longley
Seeing a definite need to add a rebounder to the side, the Bulls acquired Rodman from the Spurs, perhaps the biggest mistake in Spurs history (for fecking Will Perdue!). It's arguable that much like Deion with 49ers/Cowboys, the maverick Rodman was the difference maker. Rodman's arrival forced Kukoc to revert to his sixth man role, Harper took over at PG (position only, Pippen was a point forward, and Jordan ofter brought the ball up court), and Longley seized the starting center spot. But most importantly, Rodman brought a player that focused solely on defense and rebounding, and brought some nastiness to a front court that was softer than toilet paper.