Hi Lucy,
She is probably missing her mate. If she is rubbing her head on the bowl, she is using it as a surrogate for a mate, because her mate would normally groom her head. She may also be trying to mate with the bowl. She needs time to adjust to not having a mate. If you decide to get another bird, you can’t just put it in the cage with her. You need to have them in cages side by side, and give them a few weeks to get used to each other. If they show interest and sit near each other, then you can try to introduce them. A female budgie can be very territorial, so you need to watch them closely. Also, do not get a really young bird – try to get one around her age. If you don’t get another bird, make sure she has plenty of toys to keep her busy and give her attention daily.
Thank you for asking Lafeber,
Brenda