Bloody phones.
OP, I understand why you gave your DD your old phone for lockdown purposes, but what are you going to do with the phone now? 9 really is too young for any child to handle a virtual life. I'm guessing the 'bully' feels detached enough to be so horrible because she's communicating virtually, rather than in person. They are all just far too young for this stuff. Even adults on Mumsnet hide behind their screens to make aggressive and hurtful remarks - and we are supposedly old enough and sensible enough to behave politely and with consideration for other people.
I would also very gently suggest that you look at all the messages your DD has sent to this other girl. Many years of experience have taught me that my own children are rarely whiter than white, either in person or online. I'm not saying that your DD has been horrible back, but my youngest DC got a phone when she was 12 and I was monitoring it all the time at that point. She's now 16 and I don't monitor it - but I still reserve the right to do so, if I have any significant concerns. Just as I would have read her diary in the 'olden days', if she was causing me sleepless nights.
So far as the party goes: you do have an automatic get-out clause with Covid, so I'd use it. Not because your DD should hide behind excuses, but because if the other girl really is an unpleasant bully, she could well twist anything else that your DD says into "XiCi's DD said I can't come to her party because she hates me, when I've apologised and been really nice to her, waaaah, poor me".
Also suggest you ask DD's teacher to keep a quiet eye on them once they go back. Best to approach this in terms of "there was a falling out, and DD was very upset by it", rather than "X is bullying my DD".
Her teacher may also have views on phones and online messaging for 9 year olds.