Well known and very popular is the Danube cycle-path from Bratislava in the direction of Budapest. The ideal daytrip would be to cycle about 20 km along the Danube on the one side, to take the small ferrie at Vojka/Kyselica to other side, and to cycle back to Bratislava on the other side of the Danube.
Less known are cycle trips from Bratislava to small Austrian villages just across the border. The cycle-paths here are in excellent condition. From the border crossing Jarovce or Petrzalka you will cycle through rolling vineyards to the village of Prellenkirchen (+/- 20 km), and just outside the village there is the so-called Kellergasse or Cellarstreet, centuries old wine-cellars standing in a row of which some are open, where you can drink excellent homemade dry wines and eat honest, cold meat and cheese dishes.
The way back to Bratislava is quite tough then, but once in Bratislava, the wine will have been oozed out of your body.