Bludie,
This being a very emotional time for you currently with your relationship break-up, it might be best for you, that you do not take on too much at once.
Making a decision to let another person who has been a big part of your life go right now, might be a lot to handle emotionally.
It does not mean that you might not decide to let the friendship go down the line, but maybe you do not have to decide right now.
That she is being distant right now might be to your advantage. You can take time to heal and process the ending of your relationship. You can also tell her that you are taking some time for yourself to do just that, if she questions why you haven't been "running after her". Meaning calling her often- asking why she isn't calling you. That seems to be the pattern that she likes, from what you have written already about your disscussion or "arguing" style together.
I do think it is strange that a good friend of 5 years has started to thwart your calls after 9 months of your having moved. I moved, and have been in my new location for over a decade now, and am still in very, very regular contact (with in-person visits as well) with my very best friend who lives where I moved from.
Also, at the very time she knows that you are going through a hard time because of the break-up, and that the cycling trip might do you good, she cancels

That is
really not a good sign in my book, and I can't help but wonder if that is not part of the whole avoidance of deep discussions that she does. It would not be about you & her, but even having to get deep concerning your break-up might worry her. She might be worried about what to say to you, how emotional you might be, etc. Or, she might even think it could lead to deeper discussions about long standing issues between you & she.
Though I also wonder about another thing. Could she be feeling resentful that you moved? Just a thought...