In my experience, for what you are trying to do, the best bottle is one of those narrow necked vacuum insulated bottles. This style:

Amazon Insulated SS bottle

Anything lighter will not insulate as well. I sometimes use this style bottle while biking:

Polar Sport bottle - insulated

They don't insulate as well, but carry more liquid for less weight.

If you really want to drop weight, as Glenn suggested heating it up at your destination is probably better. If you are just making tea, you can do a lot lighter than a pocket rocket. I think you probably would end up lighter than a vacuum insulated bottle with a light weight plastic bottle, a lightweight Ti or Al cup, and a lightweight esbit burner with a quarter tab:

https://www.amazon.com/Esbit-Ultralight-...32871&psc=1

You could also swap out the esbit for an alcohol burner:

http://www.woodgaz-stove.com/fancee-feest.php