Train and Bike and Bath to Lake Neusiedl

I am planning a combined train ride and bike trip and bathing in Lake Neusiedl for this Saturday 16th.
We would take the train from Wien Hauptbahnhof Neusiedl and then bike to Podersdorf.
For those who don`t have a bike; there is a possibility to rent a bike at Neusiedl trainstation.

We will meet at 09:45 at Wien Hbf (southern entrance, which is not the entrance facing the Gürtel, but facing the ÖBB HQ building!)

Train to Neusiedl is scheduled at 10:09 arrival in Neusiedl at 10:58.
We will then ride to Podersdorf all along the lake.
This will take roughly one hour.
In Podersdorf we can visit the beach site (unfortunately there is an entry fee of 09:40 for the beach area), and stay there.
I case it is not too hot we can also continue and
take the bike ferry from Podersdorf to Rust (15,-), which runs every hour on the hour and ride from there to Schützen am Gebirge (approx 1hour) and the take train back to Vienna.
return with train at 16:36 arrival Protected content 17:36 /18:51

I will post my phone number 1h before departure

Costs for train, depend on whether we decide to form a gorup and buy a group ticket (einfach raus) or if you buy indidiually. I have a Klimaticket, so personally I don´t need to buy a ticket except for my bike.