Tourist accommodation is a cottage industry in Hungary. They have their own reservation system called Szallas similar to Booking.com. The government also give grants (loans?) to private hosts in small villages.
So I slept on the Hungarian side of the Danube on my way to Budapest. But EV6 in Hungary is not nice. It is often next to a busy road. So I chose to cross back into Slovakia where EV6 mostly a sealed road on top of the levy.
But this caused two problems: Firstly the best bridge to Slovakia was clearly only intended for motorized traffic. Fortunately, while I was looking at the map, a French cyclist showed up and we crossed together.
The second probleem was that the best place to return to Hungary was a ferry crossing. Luckily I went over the details while I was still near a bridge. And I had the common sense to realize that the ferry could be closed due to low water levels. Which turned out to be the case.