You might be able to counter-balance it with other flavors (salt, sour, sweet, hot), but you're likely still going to have some bitter notes come through, it's just a question if it's tolerable or not, and some people dislike bitter more than others. (I can't understand how people can drink beers other than lambics)
In looking at a similar thread on Chowhound, one of the recommendations is a bit of milk or cream. If you're not lactose intollerant, it might be worth a try.
This could also be a chance for an experiment -- ladle it into a bunch of glasses, try some different things (sugar, vinegar, soy, hot sauce, milk, worcestershire, combinations of them, etc), and report back to us with what you think worked best.
There are three (to the best of my knowledge) main factors at work here:
Pectin. This is a gelling agent, a bit like gelatin. Fruits such as apples and plums are very high in pectin; citrus fruits are not that high in pectin but citrus peels are incredibly high, so if you're using any of the peel, you're getting tons of great pectin.
Obviously, the more pectin, the faster and firmer it's going to gel. If the fruit doesn't contain much pectin then you're going to have to cook it down a lot or just add actual pectin (you can buy it in stores).
Acidity, as you suspect, makes a big difference. It's not just acidity, it's the relationship of acidity to pectin as above. For more details read The Role of Acid in Jelly Formation. Basically, pectin gels best at a pH of 2.5 (almost exactly the pH of lemon juice) to 4.5 (about the pH of sweet grapes).
It's best to hit the sweet spot in the middle rather than the extreme ends, so you won't generally be using pure lemon juice, you'll be adding some sugar and other ingredients. Which leads me to the final factor:
Sugar. As described in The Role of Sugar in Jelly Formation, sugar precipitates the pectin, basically making the pectin molecules less soluble which mimics the effect of a higher concentration. Therefore, more sugar makes the jelly set faster.
So: Pectin-rich fruits + high acidity + high sugar content = fast setting.
There are actually various other factors that affect the pectin (which is pretty much the only gelling agent at work when working with natural fruit jellies) like salts and even alcohol, but in the vast majority of recipes, it's acidity and sugar that are your primary concerns as well as the actual pectin content of the fruit itself.
Best Answer
The very thin outside layer of the Lime, Lemon, Orange, and other citrus. It contains aromatic and flavorful oils that will enhance your meals.
When you zest your citrus fruit (usually with a fine grater) you need make sure that you only pull off the zest and not the white pith that lies underneath. The pith is bitter and generally not something you want in your dish.