Does the Covered Bridge farm have bathroom facilities and if not, where is the closet place that has them?

Yes, also just north of the covered bridge and on the left side going towards the dam there are some older style vault toilets.

They are on River street on the south west side of the bridge at the Covered Bridge park. They are just outhouse. Water was taken out a few years ago. From the Covered Bridge take the road to the west to get to the park. Its just past the trees.

We didn't see any, but are not local and didn't stay too long. Its more of a landmark and not much in the way of parking other than a spot of gravel near one end, or shoulder of the road on the other. Not aware of any farmhouse or closet place though there is a vibrant Amish community nearby that makes furniture and whatnot.