What's the best way to take photos of a clear plastic bottle for product shots?
You want to use bright field lighting.
Have a bright white background behind the bottle, and darkness everywhere else. This ensures you minimise reflections but at the same time give your bottle some definition. You will either need a lot of space to achieve this, or some very good black anti-reflective drapes to be able to control the lighting.
If you don't have access to a studio or very large open space you will find it very hard to get good photos of clear plastic bottles.
Use a full “tent” with multiple soft lights outside.
Even the normal hole you shoot through can show up in reflections/lighting-changes on the bottles, so making a tent of drapery that exactly fits your need would be advantageous.
With a tent you have control over everything around the bottle that will be reflected. Otherwise you get images of everything in the room showing up. Even "darkness" shows, as darker reflected patches in the highlights (or missing highlights).
My bottles are shiny but not clear. In the zoomed-in view you can see remaining reflections. I used a pre-made tent and tried to blend in the softness of the "missing" patches with paper towels, other drapes, or whatnot. I also had to blend with Photoshop on the tallest bottles.
You'll have a far worse headache with clear bottles, with nothing to show except the reflections and highlights.