Senior Mom

My mom lives in an apartment attached to our home. She is 86, but in good health for her age.
She still drives some, but with senior center activities in town shut down due to covid, she has stated that she is lonely and doesn’t see any other options.
Anything I suggest is always met with a reason that she can’t do it.
I have a busy life with work, and a home and family to take care of.
I interact with mom several times a week, taking her shopping or playing games, but it’s hard to let myself think that it’s enough. When I invite her she always makes a big deal about it like I saved her life.
Knowing that my invitations are usually her only source of socialization through the week feels heavy and I end up feeling some resentment that she doesn’t do more to entertain herself as my mother-in-law and other seniors in the community do.
I think I should just give her the time I can and let her think and feel what she wants to, but I feel like a bad daughter. HELP!!!