Yes, if you can increase your speed by at least 10 feet without needing to use your Action or Bonus Action to Dash.
Per Wild Shape:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so. However, you can’t use any of your special senses, such as darkvision, unless your new form also has that sense.
Hungry Jaws is a "special attack with your bite", granted to you by your race, so you would still have access to it while Wild Shaped. There may be an argument to be made that "a special attack with your bite" is not "a bite attack", but I think the answer to that is that Hungry Jaws is eligible to benefit from Dive Attack.
You may run into an issue with speed, though. Dive Attack seems to only apply to a single bite attack, so you may have to dive 30 feet and use your Action, fly up 30 feet, then dive another 30 feet and use your Bonus action. The Quetzalcoatlus only has a fly speed of 80 feet. Thus we have to answer "does Dive Attack use 30 feet of movement," or more specifically "Is Dive Attack considered falling?" If Dive Attack is falling, then it's not a problem, but otherwise, the Quetzalcoatlus may not have enough movement to be able to benefit from Dive Attack twice in one turn.
I would argue that a Dive Attack is not considered falling since the attacking creature does not take damage. Per Falling in the PHB, page 183:
At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6.
Additionally, per Flying Creatures and Falling from Xanathar's Guide to Everything, page 77:
A flying creature in flight falls if it is knocked prone, if its speed is reduced to 0 feet, or if it otherwise loses the ability to move, unless it can hover or is being held aloft by magic, such as the fly spell.
Since Dive Attack is not any of those things, and the attacking creature doesn't take 3d6 bludgeoning damage, Dive Attack is most likely not considered falling, and therefore would take up movement, thus requiring a fly speed of at least 90 feet in order to apply the damage increase to both an Action and a Bonus Action. Multiclassing two levels into Monk would grant you +10 movement speed, or multiclassing two levels into Fighter would grant you Action Surge, which would let you Dash and make both attacks, so this is possible.