Vida Healthcare provides specialist support for up to 194 residents living with dementia across its two care homes in Harrogate.
Healthcare director Bernadette Mossman has spoken of the difficulties faced in securing Covid-19 tests for residents and staff showing symptoms of the disease.
She said one employee had been forced to go to Manchester to get tested on Sunday, while others travelled to testing sites in Hull.
The care homes, which employ about 450 staff across two sites, has also been waiting 10 days for six testing kits after the first consignment sent by Public Health England (PHE) were never delivered.
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Ms Mossman said: "The biggest issue has been delivery of home testing kits to the home. We have had a delay with that and that's been unfortunate."
She said a "number" of staff had tested positive for Covid-19, including several in the past couple of weeks.
In regard to residents, Ms Mossman said: "We have had two positive tests in the whole home, but we have not had many tests.
"We suspect there was probably potentially more residents that had the coronavirus symptoms."
Five residents have been tested in total so far. Of those, two came back positive and died in hospital in March.
Speaking about the measures the care home takes if a resident shows symptoms, Ms Mossman said: "For people living with dementia, self isolation can be a struggle because if they can't retain that information it can be very difficult.
"We try to encourage residents to remain in their room and self isolate. If that's not possible, all of our staff are having to wear sessional PPE [personal protective equipment] for the whole day, and change when they are delivering interventions to residents."
But she said residents had "embraced" the situation thanks to staff making life as normal as possible for them.
The care homes have also introduced two new static bikes for residents, which feature digital screens showing videos of scenic routes across the world.
"It's given those people the chance to have that sense of well being and exercise, which is much needed at this time," Ms Mossman added.
Dr Mike Gent, deputy director of health protection at PHE Yorkshire and the Humber, said: "We are advising Vida Grange Care Home on an outbreak of Covid-19 and have had regular contact with them since their first case was confirmed in March.
"The Government has since committed to testing all symptomatic care home residents and staff and this is being arranged for the home."
Dr Gent said when an outbreak is confirmed in a care home, PHE's health protection teams provide advice to minimise transmission.
"Additional confirmed cases do not change the public health advice once an outbreak is already confirmed in a care home," he said.
It is understood that PHE has re-sent the home testing kits.