First let's not confuse preference for "can't" I killed my first bear with a model 70, second I'm operating a rifle not as intended so is what it is.
Being crosseye dominate this is what I've found works best for me.
On a follow up shot I keep the back end of the rifle stabilized in my shoulder, my left(trigger) hand stays on the grip and my right (off hand) works the bolt.
Typically I hold the rifle with my thumb off the stock to allow the bolt to clear, but the model 70 and Mauser actions tend to require a lot more force to work and I have to grip more to reload. In the moment it's not really a conscious decision and I find every time I take a model 70 in the field I look down and find my hand bleeding.
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Probably some downsides to shooting like this but typically I have quick follow-up shots as my check stays on the stock the whole time. This is off-hand... you can imagine it's smoother on a pack.
My BIL has a couple of mauser's and I would never take those hunting, the angle of the bolt, the drag my style creates... it's just a CF when I shoot them.
If you notice in Saving Private Ryan, Private Jackson shoots lefty on a 1903A4 and has to actually reach over the action with his hand to deal with this issue.
Point being... tikka is a great ambidextrous platform.