I can recommend you the hostel called Possonium
- https://en.rail.cc/bratislava/a ... on/l/11193
It is in the city centre and just a maximum of 5 minutes away from the main train station. It was clean and okay. The big dorm was something about 12-14 EUR per night. It was the best solution to have a cheap stay in the city centre the last time I stayed there.