Long story short - he tried, but he didn't bend over backwards or anything.
When Shenkarow first put the team on the market (early 1995, IIRC), Bettman threatened him with a large fine if he attempted to sell the team before giving any local ownership groups a chance to bid. So, yes, he tried to make sure local owners would be given a fair shake.
On the other side of the coin, he insisted that any ownership group be responsible for building a new arena, and creating a fund to hedge against any future losses while the building was being built - PLUS the actual purchase price of the team. Total cost about $250M Cdn at the time, and no local group was able to raise the capital before the deadline expired (although they came close).
My personal feeling is that in the end, local owners couldn't find a way to make it work. Bettman's not really to blame, but he's hardly a saviour, either.