So I placed a beacon, then did the whole "find blueprint in beacon" then set my bot to work. My log storage was pretty far away (not in beacon range) so my bot walked over, grabbed a log, then stared blankly into the distance. What do I do to fix this?

Okay, it has this problem with bridges specifically. Only bridges, floors are fine, literally halfway across the map I can build floors, but bridges don't work.

The simple solution is to build additional storage bins near where you collect objects (such as logs) and then add one object (one log) to that bin.  By having your bin near where its object is collected, your bot won't have to walk so far to use it.