From reading your post I assume you already have built the top, meaning the bowed board is already included in the bar top. If so did you edge glue it to other boards or use mechanical fasteners such as pocket hole joinery to make the connection? My recommended method of eliminating the bow will change depending on whether the boards are alone or already made into a panel. I'll save my recommendations on this part of your question until I have more information.
As for mounting the top you have several choices depending on the base cabinets. Many cabinets have angled braces at the top corners. If these are present drill upward through them and screw the top on from the bottom. If not there are commercial table top fasteners made. These are shaped like a double "L" and screw to the bottom of the table top while the offset end fits into a groove cut into the base. If your cabinets are already assembled an easy way to make the slot in the base cabinet is to use a biscuit joiner and cut slots where the table top fasteners will fit. Tabletop fasteners link: http://www.rockler.com/table-top-fasteners. Otherwise small "L" braces available from most hardware stores will work. An advantage to the aforementioned tabletop fasteners is they allow for seasonal wood movement.
Hope this helps, Don
I also forgot to mention above, as for mounting the top if you have room use pocket hole screws. Drill the holes in the base cabinet so the screws go upward into the top. I built a side table awhile back and posted it in the projects section. There is a picture I took during assembly that shows both the pocket holes and the biscuit jointer slots for the tabletop fasteners previously mentioned. I had to use multiple methods on that project due to its construction. I used pocket holes on the back biscuit slots and tabletop fasteners on the sides and small "L" brackets on the front.
Since you did not glue the planks together to form the tabletop I suggest removing the bowed piece, drilling new pocket holes and before re-installing it use cauls or some other form of forcing the bowed board flat. Then reattach it while the mechanical force is still flattening the board. If that won't work for you my only other suggestion is to plane or sand the upward bowed portion of the board until it matches the next adjacent board. If you do not have a plane and have to sand, a belt sander can remove a lot of material in a short time.
Hope this helps, Don
Cut 4 boards as long as the top is wide. Place one set,, these are called cauls,, over/under on each end. Clamp them tight. This will draw the bow out on the ends. Inspect the joint carefully & place more cauls where they are needed. You might end up with 4-5 sets clamped on before you put the 1st screw back in. Good Luck & don't forget to post a finished pic!!