Would the airzound bike horn cause hearing damage even if used well under the duration limit?
A little differently: the 115 dB exposure is culmulative with other noise that day. So the tables tell us that if you work in an environment of 85 dB(A) for eight hours and you use the horn on your way to work, then you will damage your hearing. 

Ringing in your ears is a great warning sign from the body that you are risking damage to your hearing. 

Ear protection has its uses; you want it to bring your noise exposure down to 85dB(A) or below, which is quite difficult especially from 115 dB. It would be much better not to use the horn at all, instead of using ear plugs, because that’s a better risk management strategy. 

After all, noise-induced hearing loss is preventable.