When figuring out how to get to Liptovski-Mikulasz, check what is more convenient for you. For example, there are direct trains from Kiev to Liptovsky Mikulasz.
If you do come to Bratislava, intercity buses are quite frequent, and you'll definitely get on the right bus the day you arrive in Bratislava. But it's easiest to find out the details on the spot.
If you're more comfortable traveling by train, there's the Intercity, which runs to Košica. Both the bus and train stations in the resort itself are located in the center of town. Head towards Gurbanova Street.
If you want to drive, consider the roads on the E571/E58 route, a distance of about 200km should take no more than three hours.