[RPG] In the Hoard of the Dragon Queen adventure, why does the cult follow this road

Draconomicon (v 3.5) has the best information I have found to piece together what dragons think like and for the most part they are like geniuses that feel a small urge to eat sheep and hoard treasure.

The most important element shaping a dragon’s outlook and state of mind is time. Dragons have no desire to live for the moment; they have a vast supply of moments stretching out before them. They do not worry about wasted time. If dragons have anything in excess, it is time, and they do not concern themselves with haste. Even the dullards among dragonkind seek to fill their time by exercising their minds. Solving puzzles is a favorite activity, though the form these puzzles take depends on the kind of dragon involved. Some, such as the bronze and the copper, seek out challenging puzzles of a benign nature. Others, such as the red and the blue, contemplate a much darker brand of conundrums. They plot ways to satisfy their greed, to defeat opponents, and to gain power over other creatures. Many scholars believe that dragons owe their natural aptitude for magic to the mental games they constantly play just to keep themselves occupied.

All true dragons have great patience. They seldom hurry or rush, because they believe anything worth doing is worth doing right. For a dragon, doing something right usually involves spending a long time (from the viewpoint of shorter-lived beings) contemplating the next step.

Are just a few examples from page 25 of the Draconomicon, seek that book for more info.

As for "what does this item make you think like" is somewhat of a different answer as noted in the comments below; the item does not turn you into a dragon with all of the ancestral memories that they would possess. Thus to answer that question "what makes someone dealing with dragons more compatible in mind set?", this would have to give you greater understanding of dragons, more then most; i.e. be closer in alignment to the dragon in question and also have great knowledge on the way said dragon would act or want. The Item does not grant all of these changes but in turn twists your mind so that you simply understand the body language of dragons innately, thus when interacting with them they seem to understand you better and as a result of this understanding you also would understand them to a much higher degree. If said dragon did not know of this item or that you possessed it, it would grant you significant advantage to social encounters with them.

I would describe to my player that while using this item, he suddenly feels everyone around him seems more blunt with their actions, their words seem so plain and open, every non-dragon seems much easier to read and I would grant them a circumstantial buff to their sense motive to any short-lived race. I do not believe they would even notice the item's influence when talking with dragons as it would feel natural.

My first response would be to question whether the players know every single thing about their characters, even after the number of sessions that you have played with them. I find it very difficult to believe that there are not gaps in their backgrounds that you can use this as an opportunity to flesh out.

Looking at the list you've provided, it seems clear that these are written to be used by new characters, so my approach would be to adapt/change/use these as inspiration for bonds that do make sense for the characters you have, so that there is something to tie them into the adventure.

Take 4. as an example - surely there is one of your PCs who could have a link to a similar NPC. Similarly for 1 and 5.

I would try to view these bonds not as a limiting straight jacket, but as a tool for increasing the richness of the character backgrounds. Also, if possible then get the players involved in coming up with these bonds. There is a similar mechanic in Dungeon World and Apocalypse World where the GM is specifically encouraged to ask questions to the players to establish these types of bonds.

As for why these things haven't come up so far in the PCs' adventures, there could be any number of reasons , which is exactly why I suggest discussing and coming up with something plausible with the player in question. Maybe the reason a mentor hasn't been in touch is because they've been ill. Maybe he's been resisting contacting the PC for some reason, maybe he doesn't trust the PC for some reason but his hand has been forced etc.

So ask, 'which of you has a link to Greenest? Why?' etc. You will be surprised how creative your players can be, and getting them involved will give them a real buy-in to the story. If you do right, you're also likely to end up with a bunch of character specific plot hooks for future adventures that you can use to make the campaign much more personal to the party.