These are obviously theories, but...

Jake Earned The Leonopteryx's Respect

The Leonopteryx is referred to as the apex predator in the skies of Pandora,

GRACE

The Great Leonopteryx is the apex aerial predator. Not only rare, but the sightings tend not to get reported. Trudy makes a clicking motion with her thumb.

TRUDY

There usually isn’t time to key the mike.

JAKE

The People call it Toruk.

NORM

(translating) Last Shadow.

JAKE

Last one you ever see.

and it never looks up because it knows there is nothing to challenge it from above.

JAKE (V.O.)

The way I had it figured, Toruk is the baddest cat in the sky. Nothing attacks him. So why would he ever look up?

Jake comes up with his plan to use this as a weakness. He gets above the Leonopteryx and dives down towards it.

FROM ABOVE -- THE SMALL SHADOW of Jake’s banshee falls across the back of the mighty Toruk.

117.

JAKE (V.O.)

But that was just a theory. JAKE DIVES and WE RUSH DOWN toward the great beast and our own shadow then --

Jake lands on the Leonopteryx's back taking the Leonopteryx by surprise. The Leonopteryx has just been bested in its own territory, so when Jake attempts the bond, it submits, knowing that Jake is worthy and the union will be beneficial.

Eywa got involved

You also have Eywa - the Great Mother at work on Pandora, we see her attempting to influence things with the woodsprites

It maybe that Eywa helped Jake to bond with the Leonopteryx by giving a little nudge to the great beast.

The Leonopteryx "knew" the Toruk Macto was needed

The Leonopteryx being released at the end also suggests the bond was only needed for as long as the Toruk Macto was needed, with the defeat of the RDA the Toruk Macto was no longer needed and thus the bond could be severed. Did the Leonopteryx know that Pandora needed it and thus allowed the bond with Jake to take place?

It may be that all of these played a part, some of them or none.

How was Jake was able to bond with the Great Leonopteryx?

Jake was inhabiting the body of a Na'vi....or at least a body that was genetically identical to a Na'vi and therefore had the abilities inherent to all Na'vi which include bonding with the Pandoran fauna.

As for the Great Leonopteryx, there is no information on how Jake specifically was able to bond but bonding is not unknown...but it is rare.

Wikia

At the time of Jake Sully's introduction to the Omaticaya, no Na'vi had accomplished this for four generations and only five have managed that feat since the time of the First Songs. Jake becomes the sixth person to bond with the creature.