Bus Éireann is advising people to undertake only necessary journeys and to avoid, where possible, peak travel times on Expressway.
Capacity on all Bus Éireann buses and coaches has been reduced by 50% to adhere to social distancing guidelines.
Expressway, therefore, has 8,000 seats available daily, compared to 16,000 before Covid-19 restrictions.
"We very much regret that, despite all of our available coaches and drivers being deployed, at the moment some people are not able to board Expressway services when they wish to travel," said Eleanor Farrell, Chief Commercial Officer, Bus Éireann.
"Public health and safety is our absolute priority and there can be no flexibility on overloading coaches.
"We realise this is disappointing, and also that it can be challenging for our drivers.
"No-one wants to leave people without transport," she continued.
More than 10% of services on a number of routes have reported as being full since the end of June.
These include the X8 (Cork/Dublin via Fermoy, Mitchelstown, Cahir, Cashel); 40 (via Killarney, Macroom, Cork, Midleton, Youghal, Dungarvan, Waterford, Wexford) and 51 (Galway/Cork via Gort, Ennis, Shannon, Limerick, Buttevant, Mallow).
"Full services can be of particular concern to people wishing to travel from intermediate stops and we anticipate that demand may continue to increase," continued Eleanor Farrell.
"We want to encourage people to consider whether their journey is absolutely necessary and, especially if they plan on joining a service mid-route, to check the Expressway and Bus Éireann live Twitter feeds which will advise if the coach is full on departure."
Bus Éireann has also asked the public to travel outside of peak demand, if possible.
Currently, the busiest times are from 11am to 1pm and from 3pm to 7pm.
"There is more demand at weekends, especially Friday afternoons and Sundays,
"We very much appreciate the understanding and cooperation of customers and our staff as we manage demand through these unprecedented times and look forward to keeping people connected around the country," said Ms Farrell.
Bus Éireann has advised passengers that pre-purchased tickets booked through their website and ticket vending machines do not generally guarantee a seat, apart from the Cork/Dublin (X8) route.
"Coaches are filled on a first-come, first-served basis.
"A small number of seats are held for walk-up customers who may not have the option to book online, including those with free travel," they stated.
Wheelchair users can continue to contact Bus Éireann Customer Care to reserve a wheelchair space on a particular departure.
Once the reservation is confirmed, the wheelchair space will be guaranteed on that departure.
Due to social distancing, bus stations also have reduced capacity for those waiting for departures.
Bus Éireann asks that passengers do not arrive earlier than 15 minutes before their scheduled departure time, as it may not be possible to enter the station before then.
Since 29 June, wearing a face covering is mandatory on Bus Éireann’s services.