When should I transplant a tea rose bush?

Between these two videos, you will get good information, Deb.

https://www.youtube.com/watch?v=w_mxT4V2wVs

https://www.youtube.com/watch?v=BxZ-iE-34aA

It does depend on your Zone. Now would be the time to move it so it has a chance to settle into its new home and become established before the snow flies. Another option would be to pot the tea rose over the winter and keep in a protected area and place back in the ground in spring. See if these sites help.

https://www.gardeningknowhow.com/ornamental/flowers/roses/how-to-transplant-roses-tips-for-transplanting-a-rose-bush.htm

https://www.heirloomroses.com/info/care/how-to/transplanting-roses/

You can do this now - if your temperatures are still warm then transplant in the evening. I just did this same thing but it was in August and had great success.

Once you pull up the rose make sure you let the roots soak in a bucket of water for at least 20 minutes. Then place it in the hole where you plant to move it, fill with water cover with dirt and mulch and say a little prayer. Well that last part is optional.

Anyways I do this in the evening because the plant has a chance to recuperate when the temperature are cooler. It may wilt and you may loose some green leafs. This is okay because if you continue to care for the rose it will grow a new set and come back even better.

https://www.gardenupgreen.com/2018/08/recycled-wood-planter-boxes.html