My (34M) girlfriend (28F) is mad that I will let my best friend (35F) will sleep at my place when she visits. What can I do to make this better?

Met my girlfriend about 4 months ago, and we've so far had a jolly good time. who hang out about 3-4 times a week.
My best friend I've known for about 8 years, and we met because her boyfriend was my friend and he asked if they could rent my extra room for a short while they were looking for a new place as she was coming from another part of the country. That "short while" turned into 5 months, then he broke up with her and let her stay in my room where she lived for another 6 months and we became friends. Since then we've been inseparable, where we often visit each other's families, go travel together and such. We've never had sex or had romantic feelings for each other.
Anyway. Recently, about a week ago, I got to know something really sad. My best friend will most likely leave my city with her boyfriend and move up to his summer house permanently, which is about 4 hours away. My head has been a complete mess since then and I feel absolutely awful. The thought of seeing each other once a week to maybe, hopefully, only once a month is really anxiety-inducing but we'll make it work.
We have talked about how while it will probably be fewer times we see each other, we can make the best of it and make it better when we see each other. So when she comes to visit we can just spend the entire weekend together, she can of course sleep in my extra room, and they are planning to build an additional guest house at their summer house for me so that I can come up there and work whenever I want to.
I told my girlfriend about how sad I am, but that I'm still sure that we can get it to work and told her of our solution. She wasn't happy when I told her she would stay at my place when she visits.
She thinks men and women who aren't together shouldn't stay at each other's places, and that she should get a hotel instead. I can't ask that of her. One, because hotel prices are insane, like the equivalent of 110 dollars per night so she would spend like 220+ dollars monthly just to see me, two, she's not the most well-off earner, and three, I'm basically the only person who kept her in this city and from moving earlier. She's nowhere near close enough someone else to consider living with them.
I told her that we are old room mates and that we are used to living together, and that she has also slept at my place recently when she and her boyfriend have had fights, but she still thinks it's inappropriate.
What can I do to make this better?
tl;dr my new girlfriend is mad that I will let my best friend stay with me when she visits.


Source.