As a notorious terrorist leader, Osama Bin Laden was a serious threat to the lives of innocent people throughout the western world. Even beyond that, the crimes he had already committed were grave enough to demand justice. With that in mind, I think the time spent looking for and apprehending Bin Laden was perfectly justified.
After all the time and money we had already spent trying to find Osama Bin Laden, every additional minute and dollar spent following the 2nd Bush presidency were irrelevant from a budgetary standpoint. Once we found him, it would certainly be a waste of time to continue looking, but it absolutely was a good use of time given the outcome.
Yes, the amount time spent looking for Osama Bin Laden was necessary. He was responsible for the deaths of 2,996 Americans in the 9/11 attacks that he orchestrated. He had to be hunted down and may to pay for his actions no matter how long it took. President Bush promised it and Obama came though on that promise to the American people.
The money spent on everything in the decade after 9/11 was not simply to find Bin Laden, so the answer could be yes. While it is true that the invasions occurred because of 9/11, Bin Laden was killed in a similar fashion to literally hundreds of high profile targets, using already available infrastructure.
While Bin Laden had other followers that Americans worried would take his place, it appears that tracking down the leader was a victory for the United States' government. No death is "right," but because he was a leader who was bent on terrorizing the United States repeatedly, there was sadly not much more that could be done. It may have also brought some closure to people impacted by 9/11.