Hi
When I have a trainee, I also expect them to be using initiative by/before 6 months but don't worry it is something you can do quite easily. I know it can feel a bit daunting to just make decisions without guidance but equally we don't have time to keep asking you to do things.
I have made a handbook which stays in the surgery cupboard and one of the pages contains a list of tasks to do when you are free. Things like: stocking up the drawers, checking stock (making sure we are not about to run out of something), some cleaning tasks, bagging and dating things etc. Maybe make your own list of tasks you have been asked to do before and do them when you are free without being asked again.
You do also need to stay on the ball too, and speeding up will help the team if they feel you are taking longer to do a task than is necessary. This does of course come with time though, but sometimes you need to give yourself a push.
If you are still unsure or worried, I would ask for 10 minutes with your senior nurse and let her know you are keen to improve. Tell her about your list and ask her to add to it if she wants. then you can refer to it rather than keep asking.