Arco Bardalles

Quickly I whipped out my wand and yelled "WINGARDIUM LEVIOSA!" stopping it dead in its tracks, I could clearly see the shocked expression on its face.

The slight crunch of a leaf broke the silence above my head

I believe since the phoenix is such a highly intelligent species of magical creature, using force would only ruffle its feathers. (Pun very much intended) The bird would immediately realize your goal and probably retaliate in self defense. Since phoenix's are such dangerous creatures, I don't think any skilled wand maker would be so stupid as to provoke the bird. I think most wand makers would simply ask the bird and wait for some sort of signal that their request had been granted. Wand makers with a weaker relationship with the bird would most likely negotiate some sort of deal with the bird, as a lot of other people have commented on. Perhaps a treat or some sort of freedom/activity the specific bird enjoys.

I Hollered at the creature before breaking off into a sprint, following closely behind.