My budgie lost a few of his flock mates in recent months, and its just him and me now. He has his home set up in the living area and since that he has been mimicking more words and sounds. When the cage door is open he will fly onto my shoulder and sing. He now takes baths in front of me now (previously he would be silent and still when he would see me).
I still can see he is scared of my hand as he avoids my fingers and hands but will dance all over me and give me nibbles on the nose and sing. He isn't fussed on treats, millet, fruit, veges... nothing. Any tips?
It sounds like your budgie is starting to become more friendly and trusting of you which is great.
The key to building on this relationship is trust and go slowly .
FairyBee has given you some great links please do read them.
Those links should help, but if they don't, just let him come to you. It seems like you've made really good progress so far, I would just let him figure it out. (I personally wouldn't risk, accidentally, doing something that would leave him never wanting to touch you again. When I was training my budgies, Marllow lost balance and fell off my finger, it was back to square one after that! )
Try a toy for a reward, a mirror of stuffed animal he really likes, Marllow never really went head over heels for millet, but she absolutely adored that pretty budgie that showed up in her mirror! ; )
Mirrors are not recommended for single budgies.
Many budgies become obsessed with their reflection which can lead to aggressive tendencies and/or over-regurgitation to the reflection which is very detrimental to the budgie's health.
Stuffed animals are not recommended as toys for budgies once they are adults as chewing on the fabric can result in crop impaction from ingestion of the fibers.