I believe it is in Windows under device manager. A checkbox for listing it as a removeable device.
You'll probably have to do that with each device you plug in, but only the one time for each.
It can also be set in the BIOS, which is how I solved it on my old X58 system. I think. Been a while since eSATA was useful to me. I had an external dock, but it had to be plugged in and on for Windows to load it on boot. Was easier to use it as a USB dock.
I haven't used an internal hotswap bay since my i7-4770k, and even then I only used it for backups.