I'm not sure about bear hunts (or outfitters in the States for bear), but if you are willing to go to Canada there are fantastic opportunities there for bear. The most popular are baited hunts which usually carry extremely high success rates. Generally, the only hunters that don't score go home empty because they passed multiple chances at good bears, but were holding out for a giant, or a particular color phase. I've been on both sides of this, but always have a great time.
As a bonus, many areas offer spectacular fishing as a side activity. You fish in the morning, and head for the bear stand in the afternoon.
These hunts are what I consider a real bargain as outfitted hunts go. You can find these type hunts starting at around $3-3.5K and up to maybe $5Kish. Of course you will have travel expenses, but all in you will still fall well short of your budget...
And all the BS Covid restrictions getting in and out of Canada have been dropped.
Good luck in your search!