Lots of apartment dwellers have appropriate sized cages. In fact, I know of a woman who just moved into a tiny house, and she still has her guinea pigs in a 2x4 C&C Cage! You just need to get creative and move stuff around. Take a look at all the different cages in the photo gallery. Surely there's something that you can make work.
Also, guinea pigs need companionship of their own species. It's part of their nature. Bonding with you isn't what she needs. Part of having a pet is making their lives as best as you can, and getting her a bigger cage and a companion is part of that. In one country at least, having only one guinea pig is against the law.