Bayonet Attack

I would say yes.
As command cards override the normal rules and a bonus melee is still a continuation of the same move of that unit.

Does the "no movement reduction" also apply to bonus melee?

so the card is Bayonet Attack you can move because of that, but rather we move and we don't attack.

there is nothing on the card that requires units to attack, so it seems to me units are not forced to do so. They simply miss out on this opportunity
 

Can I use the card to move units without attacking? I would be a no for me but I have been told that it is also used in that way. The card should be, in my opinion, only used to move in order to attack and not for moving if a melee combat doesn't follow. Also because it states that if you don't have or don't want to use such units, you can order a unit of your choice. Regards.