System Information
Operating system: Gentoo Linux
Graphics card: RX 480

Blender Version
Broken: Tested on 3.2.0 alpha (as of yesterday), 3.1.0, and 2.79.

Short description of error
When baking selected to active, particle systems such as hair are not included. I am unsure if this is a bug or a feature request and apologise if it is the latter. This can be worked around by converting the particle system to a mesh and using geometry nodes to re-create the geometry; however, in doing this and attempting to transfer the vertex colours so my materials worked, I encountered another bug T96982. In newer versions of Blender where the option exists, this bug occurs both with hair shape set to "Rounded Ribbons", and with hair shape set to "3D Curves".

Exact steps for others to reproduce the error
Create a plane.

Add particle system to plane and set to hair.

Change settings to good values.

Resize default cube around the hair system to create object to bake to.

Set up image and materials for baking, with a transparent material and an image to bake to in the material of the default cube.

Go to bake tab, check "Selected to Active".

Select hair plane, then select the default cube at the same time, then press "Bake".

Alternatively, use this Blend file where all that is already set up:

Then press "Bake".