In the past, I never had much trouble fitting my somewhat chunky Bell handlebar bag (http://www.amazon.com/Bell-STOWAWAY-.../dp/B003NKS2A4) onto my trusty single-chain 7-speed bikes. Now that I've purchased my first triple-chainring bike, however, the extra "spaghetti" up front has me scratching my head. Should I just let the bag hang out in front of all of it? Will that interfere with cable action? I can't stuff it behind all the cables, because then I won't be able to get inside it. I tried hanging it inside the handlebar so that it faces me, but the straps aren't long enough.....
(2) ti TiCycles, 2007 w/ triple and 2011 fixed, 1979 Peter Mooney, ~1983 Trek 420 now fixed and ~1970 Raleigh Carlton International gravel grinder
What kind of bike are you riding? I am a little surprised the front cables aren't mirror images of the rear cables unless you are using different shifter systems front and rear.
In short, we need to know more to help you. Pictures would be great. How willing are you to look for other shifter systems? How wedded are you to that bag? It's all about priorities and choices. We can give you choices but without knowing more, we may not hit your best solution. (That solution is out there. There are many, many ways to set up shifting systems that put the shifters is quite different places, shifters of different types, ways of running cables, etc. Some of these require changing your front derailleur, perhaps both if you want to keep the shifters as a match. Some will be just a matter of making your handlebar setup slightly different, others will make the bike feel like a different machine.
OK, after some fiddling it looks like the bag will sit in front of all the cables without messing with their performance. But I should probably move the handlebar reflector so it isn't completely hidden.