As an admin it is sometimes hard to know when you should go ahead and make a decision and when you need to wait for your boss. Recently, on an admin site, someone suggested setting out every scenario she could think of and ranking whether it needs the boss's approval or not. Although I understand why she would want to do that, I thought an easier way would be to break it down as follows:
Will it impact your company?
If it is something that could embarrass your company or bind it financially in any way, this is definitely something your boss should be deciding, not the admin.
Will it inconvenience your boss?
If it is something that will impact your boss directly then it should be done in collaboration with them such as making travel arrangements, booking meetings outside of business hours or during their lunch hour or booking them with someone they have never met or may not want to meet. Things that will directly affect them should be done with their input.
Is it administrative and pertains to your duties?
This is something you can go ahead and make the decision. We make decisions every day about booking rooms for meetings, scheduling our boss's calendar, taking messages, ordering supplies. These are all things we do every day and we shouldn't be asking our boss each time something comes up.
Is it really that simple? Well, yes and no, but basically that does sum it up and is a good gauge to keep in the back of your mind. As you develop a working relationship with your boss, you will get to know what things you can go ahead and do. Some bosses want their assistants to do more than others and each circumstance will be different. That is why regular meetings with your boss are a must have. You will start to know what your boss's likes and dislikes are and when they expect you to go ahead and make the decision.
Once you do find out what their preferences are, you should write them down so you don't have to ask again and again. I have started a contact sheet in Outlook for my boss and it includes things like what seat he prefers when travelling, his Aeroplan number, whether he prefers a Queen or King-size bed, his passport number and any number of passwords he has that I need access to. This means I won't be bugging him each time when I need the information. Your boss will appreciate it.
I hope this brings a bit of clarity to this issue and helps with your day-to-day decision making.