Thanks for the trip report,
Romelle.
I wonder if your bus adventure was perhaps a one-off - say, they had engineering work on the line? (Something I'm very used to as it happens a lot here in the UK!)
www.bahn.de lists the connection as being train all the way, with a change at Sestokai.
My journey to Vilnius a couple of years ago went perfectly smoothly - like clockwork, really. Fortunately I guessed that there was not going to be a restaurant on the train (as bahn.de didn't mention one) so stocked up on snacks before setting off.