I don't think this line makes sense, because there is a difference between explicit and implicit permission.
To "authorize" seems to me to be EXPLICIT permission.
Just by being a citizen in a representative democracy you are authorising the representatives to act on your behalf.
It doesn't matter if you voted or not - if you voted you explicitly participated, and if you didn't, you said in effect, I'm happy for other citizens to make the decision on my behalf or I'm happy for the status quo to continue. There's no way to have completely clean hands as long as you remain a citizen.
The only way to get out of it is to go live in some atol in the Pacific which hasn't been claimed by any country or buy a boat and float out in international waters - seasteading I believe it's called, at which point you arn't part of any nation.
Re OP's question - No they shouldn't authorize bombing. Part of the reason Parliament voted No was because they felt that it wasn't clear whether it was really Assad who'd launched the chemical weapons or the rebels (who used sarin in May). There was a feeling that the west was being played by interested parties who wanted to use our blood and treasure for their own ends.
The MPs who voted No were mainly Labour (who whipped the No vote) but also Green, Scottish nationalists, Welsh nationalists, Northern ireland protestants (DUP), Northern ireland catholics (SDLP and Alliance), independents, some 30 Tories and 11 Libdems.
And they won. So it's definitely worth lobbying representatives instead of just giving up.
It might make you feel superior to act like it's all a waste of time, but that conceit is in reality simply a way of getting others to make the decision for you. There is no way of avoiding responsibility unless you dump your citizenship and go live on a boat in international waters (and even then you'd need to pay for a flag of convenience).