If you aren't Singaporean, PR, work/study here or have any other kind of residence permit, you cannot legally rent from private landlords. In that case hotels or Serviced Apartments
are your only option.
Serviced apartments start around S$2500/month for a studio, so I guess S$5000 for a three bedroom is usual. Try a budget hotel instead!
If a private landlord agrees to rent to you illegally, walk away as fast as you can: Since landlords get into deeper trouble for this than tenants (and he knows this!), he's probably only out to cheat you somehow. (E.g. you'd have no way whatsoever to recover your deposit if he keeps it!)
If you can legally rent, landlords here are mostly reluctant to sign anything below a one year lease, but you might be lucky if you search hard and negotiate well.
Good luck and congratulations to your wedding!