Technically speaking, the energy used by the muscles is not glycogen, but the phosphate bonds in adenosine triphosphate (ATP). When energy is needed, one of the phosphate bonds is broken, resulting in an energy release and the creation of the subsequent adenosine diphosphate (ADP) and waste materials. This is one of the main reasons that creatine phosphate works, is that it provides cells with a ready supply of extra phosphate to recreate the ATP from ADP. Glucose is part of this cycle in that it is broken down into pyruvate to feed into the Kreb's cycle. IIRC, one molecule of glucose can provide somewhere around 24 net molecules of ATP. It is the glycogen that is broken apart to provide the glucose.
Grohlier is somewhat correct, in that when muscles start to run out of stored glycogen they start relying on blood glucose and release of stored glycogen from the liver, and this can be slower than the immediate availability of muscle glycogen. However, for short burst activity such as weightlifting, the amount of time you spend in the recovery phase between sets is enough to replenish muscle glycogen from circulating blood glucose. It can take anywhere from 60-120 minutes of continuous exercise to completely deplete muscle/blood/liver stores of glycogen (This is commonly known as "bonking" or hitting the wall, another term that is vastly overused, usually incorrectly.) This time can be lengthened if necessary by eating/feeding/drinking. It's also extended by your body adapting to exercise, as your body will start to adapt by storing more glycogen in the muscles.
Recursive is correct, once the glycogen is in the muscle, it can only be used by that muscle specifically. So if you do deplete the biceps glycogen (as per your example), the triceps would not be affected much and could still do work. However, it would be impacted somewhat, as your biceps also play a part in triceps movement, and vice versa. You can't ever really work a muscle in "isolation" outside of a lab.