How to make a bicycle_repair_station visible in a layer?

I have added a bicycle_repair_station but it will not become visible in standard or bicycle layer of OSM. It is contained only in the map data.

Yes, that is the expected behaviour. The map layers on http://openstreetmap.org/ do not show all information available in the database - this is intentional, because the map strikes a balance between showing information and not becoming too cluttered.

As far as I can tell, a bicycle repair station is too specialized for inclusion in the standard map layer (the default layer). It might make sense for the cycle map layer. The cycle map layer is part of the project OpenCycleMap. The project's ticket system already has a ticket about showing repair stations: Render "bicycle repair stations" on OpenCycleMap. If you have more information to add, you can add it to this ticket.

Apart from that, there's nothing you can do to make the stations show up on the map. However, even without being visible on the map, the stations are still useful - they are searchable, and there are many other users of OSM data beside the main map, so for e.g. bicycle navigation systems of specialised maps, the stations can be useful.

Go to taginfo and search for "bicycle_repair_station". Click "Overpass turbo". Move the map to your area of interest and click "run". You'll get a map like this.

Bicycle repair stations mapped in OSM are shown on cycle.travel: for example, http://cycle.travel/map?lat=33.4534&lon=-112.073&zoom=17

(Note that cycle.travel covers Western Europe and North America, and is updated from OSM data approximately once a month.)

I did a search for bike repair and got several. These work so maybe thats the way to map one. http://www.openstreetmap.org/way/344904107 https://www.openstreetmap.org/node/3465734855

Sorry it seems you are not looking for businesses (shops) more of a self repair amenity see links below.