When traveling to and from the dojo your shinai needs to be safely and properly transported as it is illegal to simply carry one around in public.
We recommend the following stores for buying a shinai bag:
Lauwemok (located in the Netherlands) makes colorful shinai bags
Nine Circles (U.K.) sells bags for all kind of weapons, not all of which are suitable for shinai. When in doubt please double-check with a teacher whether the bag you’re interested in is suitable for kendo.