I'm a little confused.
Are you asking if we think that one round is sufficient for all game or are you asking if the rifle will shoot good with 150 gr bullets?
The type of rifle shouldn't make a difference, especially if you are shooting factory ammo.
As far as killing game goes, the 30-06 will shoot ok with 150 gr bullets for thin skinned game.
But if you are inexperienced - which I can see that you must be to question the size of the bullet.
I would go with 180 gr bullets for bears and 150 gr bullets for deer.
The 180 gr bullet will not have the same velocity as the 150 gr bullet.
The 180 gr load will kick more than the 150 gr round.
The 180 gr bullet will be a lot more forgiving if you shoot a bear in the wrong place then they 150 gr bullet.
With the right circumstances, you could probably kill a bear with a .22 rimfire rifle, but I wouldn't want to try..
The problem is that the Redfield Widefield does not have positive click adjustment.
This means that when you turn the friction adjustment - you will find that with 150 gr bullets, one line will probably equate to 1/2 inch adjustments up/down - left/right.
It is real hard to change zero from one round to the other by just counting the lines - but it can be done.
I would offer you $25 more then what you paid for the rifle and you could go out and buy yourself a bolt action rifle with a cheap scope - Bushnell, Simmons, etc.. And you would probably be more satisfied then you would with the Gamemaster.
I never shot a bear before, but I did buy a .300 Winchester Magnum rifle and a .270 WSM rifle, just in case the opportunity ever came about..