Bug Juice is a beverage.
Exactly what the beverage is varies by area, and by tradition, but it appears to always be a soft drink.
It can be as simple as red soda pop, straight up.
In some traditions, such as North American summer camps for children, it is fruit drinks(ostensibly), mixed up from powders, but that are mostly sugar, water and artificial colouring and flavour. Camp counsellors tell the kids it is made from mashed-up bugs.
Sailors in the American navy are also served a drink they call "Bug Juice." It is very sweet and contains high amounts of ascorbic acid. They will also make a paste of the powder mix, and use the paste for scrubbing and polishing steel surfaces (that the colouring in it wouldn't affect.)
Some drinks and juices, however, could literally be called bug juice. In many of them, the red, pinkish or purple colouring called "carmine" comes from the insect called cochineal. It may just be listed as "artificial colour" or "added colour."
Bug Juice is also the name of an insecticide, added to paint, made of 95.25% Deltamethrin and 4.75% Dimethyl-cyclopropanecarbonxylate. It will kill insects that crawl or land on the painted surface by poisoning them.