you can get them from shooting down normal balloons, by talking to villagers or by collecting bottles from the beach.
The bunny day event doesn't actually interfere with the normal balloons. The normal ones spawn at the following minutes: 00; 05; 10; 15; 20... You can get the bunny ones at any time.
you get them from balloons, it's not always garanteed ofc. and/or from villagers, Isabelle also gave me the cherry blossom picnic diy this morning so i think that one is garanteed too.