Why are we afraid of bass string of Bösendorfer on tuning?

I don't know, why are you?

German Sheppard's are great protection.

I just use hammers to beat them into submission.

I know what you mean, 443. Some Bösendorfers, particularly when they are new, seem ' heavier' to tune than almost any other piano, almost as though the strings are already as tight as they will go. Others on this forum will be able to tell you if they are a higher tension scale or not, otherwise, I don't know why they feel this way. I don't notice it on older Bösendorfers. I have not seen evidence of broken strings on any of them that I tune so this feeling that strings may break would appear to have no basis in fact.
I assume by your use of the word 'we' that your colleagues are also finding the same sensation when tuning them. You are not the only ones to notice this, particularly among tuners who get used to tuning only one or two other makes of piano.

I have tuned several Bösendorfers made since the 1870s, without problems of bass string breakage. You may just have come across one with bad strings.

I don't know how long it has been since the last tuning. You might try pushing the string flat first before pulling it up.