You might be better off to use sugar cubes for carbonation instead of the Fizz drops. Domino has sugar cube "Dots". A one pound package contains 198 cubes or Dots. This would be equal to 2.29 grams per Dot. According to NB's carbonation calculator one 12 ounce bottle of beer at 68°F would need 2.27 grams of sugar for 2.6 volumes of CO2.
http://www.northernbrewer.com/priming-sugar-calculator/
Check my math if you want to go this route.
Like with the Fizz drops you won't need a bottling bucket or measure a sugar solution with a syringe for each bottle.
You definitely don't want to add the sugar solution to the fermentor and then stir. This would bring up the trub which will end up in your bottles.