Using a French press with finely ground coffee I usually make two grinds for my coffee - a fine grind for my Moka and a coarse grind to take to work so I can put it in a French press.

Today I zoned out and ground everything finely, and I don't have beans left for another batch. I've tried using my Moka grind in a french press before, but it always tastes burnt or extremely bitter.

Is there a way to make coffee using a French press with finely ground beans, without it becoming bitter?

This question seems quite similar, though the answers deal more with the sediment than the taste of the coffee itself.
If you use immersion brewing (which is what a French press does) with more finely ground coffee, you will want to reduce the time as extraction is faster.  I wish I could give you an exact time, but I have not experimented with this; I would start with approximately 2 minutes.

You are also likely to ge ta muddier, grittier cup as the mesh in the press will not catch all of the more finely ground coffee.