Technically speaking, the dungeon finder system does not work with gearscore. Which means that gearscore cannot offer an exact nor appropriate estimation as to which point you should be able to queue up. For standard heroic dungeon finder, you will need approximately 180 average item level. The quickest way to boost this is to replace your lowest item level items with higher item level items. You could be wearing full 219 item level items, except for a single white pair of boots with an item level of 1. That can massively hurt your average item level, despite having a gearscore value of 4k. Gearscore doesn't average your gear overall, but instead applies a static value to an item and whatever enchants and gems that can be applied to it.
So, if you're having problems queueing, I would suggest that your first step to be replacing any green or white quality items you might be wearing up to at least blue quality.