In a medium saucepan combine 1 cup of the water, molasses and the sugar. Bring to a boil to dissolve all of the sugar and remove from heat.
Carefully remove the peel of the lemon, leaving behind as much of the white pith as possible. Add zest to the hot sugar syrup and cover to steep 10 minutes.
Meanwhile, break up celery and add to a food processor. Pulse until very finely chopped or even until slightly mushy.
After lemon peel has steeped in the syrup, add remaining water. This will cool the syrup almost immediately. Add celery and juice of the lemon. If the mixture is completely cooled, add ginger bug and mix well.
Strain the wort into a large measuring cup with a spout for easy pouring. (This soda will have a little harmless murkiness to it; if you do not like this, strain through cheesecloth for extra clarity.)
Transfer soda into 2 one quart bottles with swing top seals or into recycled plastic soda bottles with screw top lids. Do not fill more than two-thirds. Close tightly and place in a warm location to ferment, about 1-5 days. This may take even longer if location is too cool.
Once soda is carbonated, place bottles into refrigerator to chill. Serve over ice. Celery soda will last for 2 weeks in the refrigerator.