It's difficult to suggest alternatives, there is always walking since Dublin has a relatively compact city centre with few hills, DART rail services are still operating along the coast from Malahide and Howth to Greystones. The two non-connecting lines of the LUAS are also running from south Dublin to St. Stephen's Green and from Tallaght in the west to The Point in Dublin's Docklands. You can always pay a taxi driver to take you on your journey. Dublin Bikes are a good idea for short city centre journeys but you have to register to use them.
Getting to and from the Airport is easy, forget the Dublin Bus services and use the always friendly Aircoach who have several routes through the city to Dublin Airport.
Bus Eireann services throughout the country are also still operating and there are several private companies operating many intercity routes as well.
Not sure at the moment how long the strike will last, but it isn't set to end soon. If you're visiting Dublin in the next week or are already here, send me an email or leave a comment and I'll be glad to give you some advice on how to get around.
Well the 3,000 staff at Dublin Bus will return to work tomorrow, Wednesday August 7th, so hopefully all you visitors to Dublin will be able to go about your holidays in normal fashion.