If there are strong crosswinds, riding slowly makes you less stable, not more. In addition, you need considerably more buffer space if you get pushed sideways and you need to get lower on the bike so that you are less of a sail. In particularly windy conditions you will need to countersteer and lean. Grip the bars firmly, but not a death grip.
I'd be of the opposite view - having a narrow cycle lane within a bus lane makes conditions worse for cyclists, not better.
In principle, cyclists should not risk their safety - "even" if this means delaying another road user by a few seconds....
My instincts tell me to slow down and be closer to the side. Certainly keen to avoid getting sprawled on a major lane. A cycle lane reduces kerb hugging by buses and most vehicles except for black cabs.