How close to a tree should I put a hugelkultur bed?

Trees in the desert where I live are generally very slow growing and small in size and number so I can't afford to risk hurting any of them. I've started collecting and piling up dead woody material to make my first hugelkultur and am wondering how close to a living tree wold be acceptable to build the bed? Do I need to avoid building on top of where the drip line currently is or where I eventually hope it will be?

A tree can benefit by being close to a hugel culture bed especially in the desert if planted on the lower side of the hugle culture to profit from the extra moisture.  

Now you might want to make sure that you have walking space between your tree and hugel culture bed.  Also, the sun has a factor.  Do you want some shade from the desert sun on your hugel culture bed.

Best to choose plants & trees that are appropriate for your climate.

To work well in desert, hugelkultur need to be very large (I'm guessing 6 feet tall or more).  I had no success with the technique in my less-dry-than-yours climate.  I have had good success with buried wood beds.  I would not use either technique within the dripline of an established tree.

https://permies.com/t/52077/Buried-Wood-Beds

The tree is only about 4 or 5 feet tall and I'm going to make the hugel about 8 feet tall so. It'll be quite a while before the tree provides shade. Assuming I don't run out of woody materials, I'm also planning to do some buried wood beds in some other areas where I can actually dig with a shovel.

I'm finding that the soil is so dry that it is quite difficult to get it to pile up so it looks like I'll be digging and burying instead. Another option I thought of would be to build a dry stacked rock wall around the hugelkultur to help hold the dirt in and reduce the drying effect of the wind. Thankfully the wood I've collected so far is piled up on one end of where I am making the bed so I'll just dig in the area not yet piled with wood first transfer the wood to the hole and then dig where the wood was.
I'll be digging mostly with a pickax since it is very rocky. I'm thinking of removing rocks in the size range between a green mango and a Geo Metro. Clumps of decomposing granite I'll probably just throw at a solid rock to make them crumble into bits and put them back in when I replace the soil. Would there be any benefit to putting the larger rocks back in as well?

You might consider putting your hugelkultur where it could profit of gathering extra moisture from run off rain water.

For example, if you have 8 inches of rain annually, but you profit from the rain water run off, it might be équivalent to 20 inches of rain.