I feel awful not letting my cat in my room

We adopted a 14 year old cat today (our family always adopts older/sick cats to give them some good twilight years) and she is super sweet and affectionate, the loudest purrer I have ever seen but she has one problem. We got her from a shelter after her previous owner unceremoniously dropped her off.

We live in an apartment with 2 floors, the living room, bathroom and kitchen are upstairs and the bedrooms are downstairs. We prefer keeping her upstairs cause that's where the litterbox, food and everything is. We'd rather keep her away from the bedrooms because hair on the beds and all that.

We have had her for a couple hours now and she is settling well, but she has seemingly fixated on my bedroom and getting into it. She got in earlier and I snuggled her on the bed for a bit right after she got home and now she seems insistent on getting in. I am doing the usual cold shoulder of keeping her out and just shutting the door and ignoring it, but she'll scratch at the door and try to push it open and it is breaking my heart.

She is probably just finding a place in the house she likes and I am sure that once she sits down on the couch she'll love it but is this a thing we should take care of ASAP?

Do I just keep powering thru it or are there other ways to get her to stay upstairs that we can start early now that she's here?