I use chlorohexidine too (sold as the brand Nolvasan - you can get it at places like Tractor Supply but it's not cheap), but I will be switching back to bleach as soon as this bottle runs out. It's too expensive for my taste whenever I can do the same thing with a cheap bottle of bleach. Once you dilute it to the recommended amount, it should last you for a long time.
Follow the directions on the bottle too... a lot of people just wipe things down and assume they're clean but the directions on both say to leave the item submerged for ~10 minutes.
I've also heard of people using vinegar, but I can't imagine how bad the smell would be after awhile.