Although it is sensible, especially at first, to have most work done by a dedicated string instrument repairer or shop, there are a few things that anyone can do at home:
Never forget to wipe clean the instrument and bow with a soft, clean, natural-fibre cloth after playing (a good quality household duster is fine) to remove general dirt and, more specifically, the dusting of rosin that collects on the belly of the instrument and the bow. Take care to clean between the strings and the fingerboard, and also under the fingerboard. This is not simply for cosmetic reasons - the rosin will eventually permanently flatten the shine on the varnish if it is not removed promptly.
Perhaps once or twice a year, it's a good idea to clean your bass with an appropriate instrument cleaner. Although you should try hard to keep the cleaner away from the strings, it's advisable to clean them afterwards anyway, along with the fingerboard, which tends to get a degree of rosin building up on it, particularly at the top end. For this, surgical spirit works very well, but make absolutely sure you keep it away from the varnish, as it will dissolve it!Re-hairing the bow is one of the regular jobs that should be done by a specialist shop or repairer. It's important not to leave it until large numbers of hairs have broken - as the hairs tend to break progressively from one side, the end result is that the stick will bow out the other way when the hair is tight, eventually causing permanent distortion.