Why is my icecream bitter?
It's no surprise to me that you describe the final taste as being similar to a raw gherkin, because both melons and gherkins are closely related to the cucumber.

Melons actually do have bitter notes; according to McGee, they contain "green, grassy compounds" as well as sulfur compounds, the latter being the same sort of thing you'd find in garlic.

Since melons only get sweeter on the vine, I would assume that the general blandness was caused by the melons being harvested too early and possibly sitting on the grocery store shelf for a long time.

If there was noticeable bitterness beyond what you tasted in the raw fruit, it was probably just because you got a concentrated dose of it in puree form.  Overcooking it would also increase the bitterness, but you say it wasn't exposed to heat (could the custard still have been very hot when you incorporated the melon?).

There is no way it was a reaction with guar gum - it's a very common additive in melon-based drinks and desserts.  It's also extremely unlikely to have been a normal reaction with the cream; I've made melon mousse and other dairy items with melon and never noticed any kind of unusual bitterness.

The only other possibility I can think of is that there may have been a problem with the cream itself.  This varies quite a bit from brand to brand and region to region, but most of the time, the "cream" you buy does not just have cream in it; for example, I'm looking at a typical supermarket carton that contains cream, milk, skim milk powder, dextrose, and a bunch of E numbers, and even some sodium citrate.  These creams can easily take on bitterness before they go sour.  So if you were using the typical supermarket brand of heavy cream, and it was sitting in your fridge for a while, that may have been a contributing factor.

All in all, I think it was probably a very random and unfortunate combination of factors that would have been due to the specific ingredients used rather than the types of ingredients.  I doubt you'd get the same results if you tried again with fresh melons, cream, and eggs.