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She will need a visa to enter the UK. Not simply a letter.
How long is she planning to visit for?
She is basically applying for a standard visitors visa. It is a straight forward process and I attach herewith the link to the forms - https://www.gov.uk/standard-visitor-visa/apply
I hope that this helps and please rate positive.
There really is no need at this time to write such a letter. You do not need to 'invite' her to visit or indeed confirm that she is your girlfriend for the purpose of a standard visitors visa. Please rate positive.
I see you have not rated yet. Is there any other questions that I can help you with?
I would be grateful if you could please take a second to leave a positive rating (3, 4 or 5 stars) as that is an important part of our process and recognises the time I have spent assisting you. If you need me to clarify anything before you go - please get back to me on here and I will assist further as best as I can. Thank you