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You can take your bike on a train to Vienna. From ΓBB website (the national railway system of Austria):
"Regio-Biking" stands for the transport of bicycles on the following trains: Regionalzug (R), RegionalExpress (REX) und S-Bahn.
"Regio-Biking" cannot be booked in advance. Acceptance is subject to the availability of bicycle bays. To allow for maximum flexibility, you will have to load your bicycle yourself when using "Regio-Biking".
Also for travels with the EURegio Ticket to neighbouring European countries (Czechia, Slovakia, Hungary), the price for bicycle carriage is already included in the ticket price.
If you would like to search for trains, on which you can take your bicycle with you, in the Online Schedule Information, simply tick the checkbox "Bicycle transport" in the query screen.
www.wien-vienna.at offers transport by boat between Vienna and Bratislava. One way ticket costs 23 EUR and bike transport costs 4 EUR extra.
Upvote:2
By train:
There is a train Bratislava Main St. - Vienna Main St. every hour. Bikes can be taken without extra charge. (Adult fare was 13β¬).