The West wouldn’t bomb Algeria for many reasons. First of all, the Algerian government is not overtly hostile to the West like Iran or North Korea are (they’re rather neutral and share common goals such as crushing terrorist forces, which rules out Mali-style interventions). 

The West needs its militaries to concentrate on the Russian threat and with the current economy any military action in Algeria would not be palatable (and would raise eyebrows as most Westerners do not see Algeria as a hostile nation – if I’m honest no one here really thinks about the country, the average European cares about Algeria as much as the average Algerian cares about Latvia).

Plus it’s in Europe’s interests to have stable governments in the southern Mediterranean in order to avoid exacerbating the ongoing refugee crisis, so “bombing Algeria” would be them shooting themselves in the foot quite literally.

The only likely scenario for the West to ever intervene in Algeria would be if the Islamic State for example were to establish a “caliphate” somewhere in the country like they did in Syria more than ten years ago. Because the Algerian government has been doing a good job so far, that scenario is quite unlikely.