Minigun, you are somewhat mistaken. The Lewinski saga came AFTER the US was already in Bosnia, boots on the ground. Check, your years, mate, the winter of 1995 is when US Army units road the rails and roads into Bosnia, and the fall of 1995 was when Dayton Agreement got hammered out. The blue dress and the blow job was after that, and the criticism on him was more closely linked to later operations in terms of that whole "wag the dog" mess. The year 1998 was when the Monica thing came to a head, so to speak.
Clinton wanted to get into Bosnia to help out sooner than he was able to. He tried to but he ran into trouble with Congress, blue helmets (backlash from the mess in Somalia, see also the Michael New case) and the funding of US ops (no the world's policeman anymore, Cold War is over) between 1991 and the eventual decision to get involved after the Dayton Agreement.
One of many problems to overcome with Congress vis a vis a Bosnia operation sooner was the already fecked up UN RoE dual key stupidity. The more rational argument was that you can't keep the peace if there is not first a peace keeping agreement. (That was actually a good point). Dayton put that to bed and in we went, under NATO RoE and not so much UN interference in basic functions. Note that in September of 1995 USS Normandy launched Tomahawks on Serbian air defense positions, which got the French and Russians crying for some political reason or other. That was also under Bill Clinton, and Admiral "Snuffy" Smith.
There were other issues that got domestic political opponents arguing against direct intervention. Some of this stemmed from Bosnia being the usual messy UN operation (UN was into Bosnia long before the US showed up with big units in NATO ... and there were some US support folks supporting UNISOM and UNPROFOR previously ...).
Before our boots were on the ground in Northern Bosnia, ops as Sharp Fence and Maritime Guard finally merged to become Operation Sharp Guard. (The arms embargo on FY had been supported by the US for some time).
It was very much "Clinton's War" to some partisans in the GOP, as was the Kosovo thing. The fact that he finally got some bipartisan support after a few years of trying is, of course, overlooked by same partisans in the GOP ... my own criticism of Clinton on Bosnia at the time was the impression he left of being led around the world by the nose by one CNN reporter named Christiana Amanpour. I am off topic, so I'll save that for another time.
The President who unequivocally would NOT go into Bosnia was President George H W Bush. He passed the torch, as well as the mess in Somalia, to Clinton in January of 1993.