We can’t force our friendship on another person, but we can let them know that we care about them and want to help them if they need us. And this may be the best you can do in this situation.
Don’t give up, however. God cares for your neighbor — and so should you, even if she seems indifferent. Some people are just shy; others may be suspicious of our motives; still others may simply not want to be bothered. But whatever her reasons, God put you next to her, and as you have opportunity let her know you care. The Bible says, “If you really keep the royal law found in Scripture, ‘Love your neighbor as yourself,’ you are doing right” (James 2:8).
This is especially important because of what you say about her age. Like many older people, she’s probably very independent and is determined to stay in her home as long as she can. But time takes its toll; gradually she may lose the ability to take care of herself. Or she may experience a fall or sudden illness, and will need your help.
Pray, too, for your neighbor, and ask God to help you be an example to her of Christ’s love and compassion. In addition, see if you can find out anything about her relatives, in case you need to contact them in an emergency. Even as He was hanging from the cross, Jesus made sure that one of His disciples was willing to provide for His mother, Mary (see John 19:26-27).