No.
I have VERY limited unarmed combat training (just hip-pocket stuff from Ft. Knox), aside from wrestling, which ain't exactly the same. I'm also a fencer, which has maybe a little in common with bayonet fights.
HOWEVER, a rifle with a bayonet fixed is a much more potent weapon in hand-to-hand than a knife, especially against an opponent who likewise has a rifle and bayonet. You need your rifle not only for the added reach, but to parry the thrusts and slashes of your adversary. Plus, you have the added weapon of your rifle butt, which could come in very handy.
If you were in a situation like that with a knife against someone with a rifle and fixed bayonet, I'd really suggest running, it would be like going aginst someone who has a bat with a set of brass knuckles, it just ain't gonna work out for you.