I would not say I am trying to "manage up", but I am definitely trying to be a lot more active in my growth process. In the past I kept waiting for things to happen, and thought my manager would have all the answers. Now, I want to be an active part of that conversation and find the right path.
You will actually be helping them if you can package up "asks" in a way so that all they have to do is hit reply on an email, type "approved" and hit send. There's often an asymmetry between the value you get vs. the cost to your manager which you can exploit. For example, where I work they provide financial support for certain forms of further study (e.g. master's degree) in certain domains. If one of my direct reports sent me an email explaining they want to study X and the policy covers them studying X, here are the details etc. etc. I will say "approved" pretty much every time. The money doesn't come out of my budget anyway, so it's free additional remuneration frommy perspective. Heck, even when it is my budget I often don't care because it's not personally coming out of my own pocket, and we lose that money anyway once the next financial year ticks over, so better to spend it while we can. But if they just sit there quietly hoping that I'll one day come to them with an offer for them to do further studies in X, they're going to be waiting forever. I want to give my team members stuff but I've got 50 billion other things to content with so I don't have the time to plan their career for them. The worst are the people who think I'm their mother and they come to me with "I want this thing, now you go figure out how to do it for me." The thing is, I'm lazy: I like to do easy things, and I don't like to do hard things. And that request sounds like a lot of hard work to me. Easier to just say no.
So remember: (1) If you don't ask you don't get, (2) It's almost never my money anyway, and (3) If you make it easy for me to say "yes", I almost certainly will.