Influences are locked during conflict, but losing the battle counts against your chosen factions 7-day 'war counter' slide scale, where the eventual winner will gain 4% & the losing faction loses 4%, or something like that.
Bonds handed in - not sure, but I expect someone will be along shortly who knows.
from what I can gather, though, if you were operating in a vacuum (ie. no other CMDRs are acting on either side of the war at all ever in any way) and that was your sole participation that day, then it might balance out, because NPCs aren't turning in bonds. I'm just not sure what the specific influence gain/loss is for each of those events. Feel free to let us know whether your faction lost or drew that day.
If you lose the occasional battle, don’t stress. Your overall daily contribution of Bonds, Wins, and Objectives will patch it up. Move back to the Low CZ and grab a couple of easy wins. Those Spec Ops NPCs can be punishing when they gang up on you.