The best I can tell you is to just to keep the Streetpass on and the 3ds on or in sleep mode when you go out and hope to Streetpass someone with the ticket eventually. Otherwise, the GTS is great as long as you offer fair trades. Fair trades happen so fast that you will often only see people asking for unfair or impossible trades. If you are going to offer starters or fossils, you should know that since so many people offer them, it might take some time before someone sees yours even if it's a fair trade.
If you'd let me share a personal story on the GTS, I had once deposited a Seadra in it's 70s holding a Dragon Scale. What I had asked for in return was a Terrakion, a Legendary Pokémon. The trade had to have happened in about 5 to 30 seconds and I now had a new Terrakion. Funny thing is, I was planning on trading the Seadra to myself so I could get a Kindra, I had given it the moves I wanted and EV trained it in the areas I wanted. I only asked for a Terrakion because I had one in my other game and I thought asking for a Legendary would take some time for someone willing to trade. I had my game right next to me after I finished the deposit, so I switched the games as fast as I could because I really didn't want to chance being too slow on the Seadra I trained. But when I searched for my Seadra, it wasn't there. I thought "there is no way it could have been that fast," but when I switched back to check, I saw that message, "The Pokémon you deposited was traded!" In the 30 seconds it took me to switch my games and turn on the GTS, someone got a battle ready Kingdra and I got an extra Terrakion I didn't even need. My best guess on how it was so fast is that the person who had the Terrakion already deposited it and asked for a Seadra, so when I deposited mine the GTS must have traded automatically. I was inconvenienced, but I ended up hatching another Horsea, EV training it again, and giving the new Seadra another Dragon Scale, only this time I used the other game to deposit a weak Pokémon and asked for that high level Seadra. So the GTS can be useful for evolving your own Pokémon too or trading items to yourself, if you're clever with it.