You can never go wrong with a 30-06. I have one and it's my all around 'go to' rifle. It will put down pretty much everything in North America. You can get heavier bullets for elk, and lighter bullets for antelope. Mine shoots 165 grains beautifully and it's an all around good bullet weight for pretty much everything. I've killed elk with it and didn't feel undergunned as well as antelope and didn't feel overgunned and it did well. You never know when you're going to want to come out west
Agree with everyone above. If bear means grizzly then go with a 300 or 338 win mag. I don't own either but have shot both. To me the 338 is really underated and not as much recoil as the 300. If bear means black bear then anything mentioned should be sufficient. The only advantage I see to any of them is the 308 can be had in shorter faster handling guns depending on what style bear hunt you are doing.
Then obviously nothing smaller than 375 caliber is sufficient. Besides that way you're covered in case of a rogue elephant in your subdivision. I'd prefer h&h, but kinda like some of the stainless 375 ruger guns.
My current elk gun and all around rifle is a 30-06. I used a .325 WSM for years and loved the gun but got tired of paying $70 for factory ammo since I didn't reload. I sold the gun in a moment of mental disability thinking it was a good idea. I still regret it. If I didn't own this stinkin practical '06 I'd be spending money on a 300 Win mag or a 300 WSM. Or..... a .260 or 6.5x55 Swede is also beckoning to me seductively.... I think in your case, I'd go with a .260 and then take the -06 on the bear hunt. Best of both worlds. New gun and still have plenty of firepower.
A 25-06 would be a nice deer gun, and also perfect for antelope if you come out west. I wouldn't use it on a bear, but as an excuse to buy a new rifle... Also a 30-30 is just an awesome rifle to have since everyone should have a lever gun and will do both the deer and bear.
Gotta love the new hunt, new rifle!! Since you have an '06 and will be hunting black bear and want to use it for deer maybe look at one of the .284 calibers.... .280, .280AI, 7RM, 7STW, flat shooting, plenty of choices for ammo and it'll give you a little something different in the safe.
If you want to go bigger than the '06 then I would say just make the jump up in diameter to a .338-- .338 federal, .338RCM, .338wm, .338/06?