Okay so I'll reason w/ acids to understand the stuff about bases. The O polarizes bonds more b/c of its increasing electronegativity meaning that it is more likely to lose a proton (ie H2O is more acidic than NH3).
Interesting idea but I've always heard it described in terms of the stability of the base or acid. I'm not sure describing it directly in terms of bond polarity is consistent with this reasoning.
For example when comparing the acidity of H20 and NH3 we say that H20 is the stronger acid because its conjugate base OH- is more stable with a negative charge.
With H3O+ and NH4+ it's easier to think of it in terms of conjugate acid stability. H3O+ is less stable with a positive charge and therefore is the stronger acid.
This would mean that NH3 is the stronger base, probably the nonbonding electrons on the N are more available for attracting an acid.
This last sentence kind of sounds like you may be confusing how nucleophility with basicity. Ammonia's basicity should be described strictly in terms of its stability with and without an extra proton, not how easily the reaction occurs.