truly scared the pants off me when I was drifting outwards uncontrollably towards a National Express coach .
That is a worry, and shouldn't happen. It does make me wonder if you are always in control of your bike.
Considered controversial by some, but in fact it's the only way to turn a motorcycle that's moving rather than crawling. Counter steering;
Wanna go to the left, then push down on the left bar (or pull back on the right bar)
Wanna go to the right, then push down on the right bar (or pull back on the left)
Plus never get fixed on where you fear you are going, always look where you wanna go. Combine these two techniques, if you haven't already, and you should hopefully always end up going where you want to go, even on nasty tyres.