I’ve been a terrible friend

In the time where you haven’t called or reached out to her, has she reached out or tried to call you? Friendship and communication are a two-way street and the onus is not on you to put in all of the effort, if your friend wanted or needed your support she could have reached out. Your friend sounds self-centred and is being unfair to put the lack of contact solely on you if she hasn’t made an effort either.

Op..... you havent been a great friend, which is not ideal, but the important thing is that you've been honest with yourself about how you've behaved.

Now you need to be honest with your friend. Apologise to her. Tell her she's been a great friend to you and you've let her down massively and you don't blame her for being hurt.

I'd send her a bunch of flowers and ask her if she's up for a phonecall and maybe a catchup....and take it from there.

So many people do wrong but never admit to it. This is your opportunity to help make it a bit better for your friend and for both of you to potentially mo e forward.

Kudos to you for being honest about what you did wrong.

To be fair I wouldn’t expect a long distance friend to be looking after me in that situation, I’d lean on people closer to home.

I would say give yourself a break. People come and go in our lives through no fault of anyone’s. Life gets busy and living 5 hours away is a huge challenge. From what you’ve said you genuinely didn’t know what to do for the best in this situation.
Why not write a letter to the friend and explain your feelings? Do give yourself a break. It’s hard to support someone going through grief and it sounds like you are an easy target for her just now while she is still struggling.