I received a plant from someone I have been gifting. The problem is her whole property is full and..

If all the bush buttons are grayed out, it means they have no space on their island, and there is no way to leave a bush. Try again another time.

If you are able to select a bush, it means there is a free space somewhere, but you'll have to find it manually (until the developers fix this glitch). Sometimes it may help if you close the bush selection and move to an area of island with more space and try again.