It should be possible, can you link to the bundle where you’re not seeing the option?
Viewing post in Buying a bundle as a gift
I looked at a bunch and didn't see the option on any of them. A few examples (screenshots):
https://itch.io/s/46190/lunar-new-year-2021
https://itch.io/s/45658/lunar-new-year-2021
https://itch.io/s/45553/-lunar-waifu-bundle-2021-
In contrast, buying this game from its sale page (which only has 1 game) shows the gift link (screenshot):