Burn definitely seems like one of the major challenges for Faeries. I don't know, though. Giving up on Bitterblossom is giving up one what makes the deck actually tick. Without it, you're just playing a control deck that happens to run faeries, and you lose synergy with Scion of Oona and Spellstutter Sprite. I'd rather try to offset the life loss with equipment ( Loxodon and Sword of . . . I forget which one ). Even if you don't get to attack, any burn spell eaten by one of your creatures is one less for you. Leyline of the Void and various artifacts help against the dreaded Snapcaster, too.
Still a challenge, but I just don't see giving up on BB as being the solution. If your opponent decides to burn you, then you'll easily offset the life you lost by hurting your opponent with the fairy you gained. And since you're not paying mana for your creatures at that point, you can spend it on counters and removal. If it comes to that, you can even use your Mistbind to Champion BB. If you live that long, anyway.
I scored some faeries today. Vendilion Clique and a Scion of Oona, as well as a Cryptic Command. Also, some useful lands. It's happening!
I also sat across from someone trading a Mox ( not sure which one ) and a Time Walk. It was pretty ridiculous.