So in the evening when my budgie is getting tired, sometimes she will let me lightly pat her tail when it sticks out of the cage, where as during the day, she'll jump away as soon as my hand comes near the cage.
Then last night while I was covering the cage she jumped up onto the side of the cage and hung there for a while. At first, I slowly placed my hand on the cage near her and she sat there quietly and didn't try to jump away like she normally would. I able to lightly touch her stomach and she once again, did not jump away.
I realize this is likely because she's getting sleepy and is more docile than usual but the question I had was whether or not this could be detrimental to me taming her. She doesn't seem to distrust me any more than usual during the day time, in fact she seems to be slowly trusting me more but I don't want to continue to try to tame her in the evening if the reason she isn't jumping away is because she's simply too tired to and won't build trust.
There's some great tips for bonding with your budgie on the stickies here which you can browse through for some hints to help bonding.
I think that as long as your budgie can see what you're doing, like with stroking her chest, and she doesn't move away this is a great step to bonding with her. I would just be careful with stroking her tail as it might startle her if she doesn't see you.
I know that you shouldn't stroke a female budgies back either.