Except for not answering your phone, I think you made good choices. The fact that your Mum rang many times suggests to me that she was VERY concerned for your welfare, and was imagining that all kinds of horrible things had happened to you - irrational perhaps - but true. You added fuel to her fire by not speaking to her ... that was inconsiderate. I suggest that a better way forward would be to write down (as a help to you) when you speak to her, and you should speak to her - what your thought process was. Something like: I was faced with a new set of circumstances, I know that I am going to have to deal with stuff like this - so I tried to make the best of a bad lot. As you know __ lives just around the corner from where I was going to meet __. I felt disappointed about the messed up the arrangements, I didn't want to worry you ... I know NOW that not answering the phone was the wrong thing to do and made you worry more : SORRY! Parents are rarely thinking ,what you think they are thinking, I would imagine she want's to shock you with the grounding. Ask what she would have preferred you to do in the situation.
It is a tough time but you are approaching everything from a different place than your Mum she still wants to protect her child (of any age) from the horrible world. However you are young and fearless and up for the challenges the world has to offer - a little consideration goes a long way to bridge that gap ! Try to imagine how you would feel if you were in your Mum's place- she let you go on a bus at night - then she couldn't contact you.
I have two teenagers one is organised and always has their phone, leaves a timeplan on the fridge,then sends text updates to house phone if things change! It's great.. My other child is the opposite and is a constant worry ... so I ask lots of questions, can cause more friction. I would be impressed that he thought to get help from a friend, and would hold this friend in a higher regard too!