They're not that hard to win over; they like the sound of voices, and watching moving things. Tell one a story. It will listen with its wings tucked around it and its head tilted, following your gestures. One story, that's all it'll take, and the guardian will come right up to you and cuddle, even purring a bit. If you climb on its back it will probably take off and fly you high, circling around the mountain.
If it still doesn't let you inside the caves when you land, it's only a matter of time. Give it a few more ear scratches, maybe talking to it while you do, and it will let you pass unimpeded through one of the entrances and into the mountain.