There are actually a number of different adult day care transportation options a senior has depending on what is available in your community. Many churches and nonprofit organizations offer volunteer driver programs. They are usually free or low cost.
Most communities have paratransit services with small buses or vans that provide door-to-door services. There are some transportation programs especially for seniors with mental or physical impairments. They will cater to the needs of your senior, helping them into the doors of their destination if necessary.
Does your community have Uber or Lyft? These are smartphone apps that connect riders with a driver for a generally low fare. Some healthcare providers are even partnering with rideshare companies to transport elders and patients to medical appointments and elsewhere.
To find the transportations options in your community, talk to your local aging agency.