Just because it says "BSN preferred" doesn't mean they won't hire someone without a BSN. It could very well mean though that if both a BSN applicant and a non-BSN applicant apply ...... if all other qualifications are similar and they need to chose between the two, then they'll most likely pick the BSN applicant, since that's what they "prefer".
Employers can "prefer" many things. BSN, bilingual, etc. But there's only so many applicants that have all their specific preferences, so they're not always going to get exactly what they want.
I agree that the fact that you're working on your BSN is really going to help you. APPLY! There's no harm in applying. Don't sell yourself short. You say you only have less than 2 years experience, but that's a decent amount of time. You've got bedside experience and you're working towards a BSN ..... I say go for it and apply, see what's out there! Good luck to you