I don't think Bella would have neccasarly had a bad a time as Edward did.
Most of Edwards objection comes from his belief in his soul, which is probably linked to his spiritual/religious background. If I remember my history correctly even in Edwards time apperance in public for a man where still important. For Bella back then she might have been draged to church but her belief would have been of little importance. Edward would have been taught more stictly and told he was incharge of his salvation where as Bella would have been dragged along and just told to believe this or that. In short Bella might still have had a very different philosphy on the soul. (hope I explained that right)
Of course she would still freak out but she wouldn't have spent as many years worrying about her soul and she would have probably started sooner on trying to do something good with her immortality, like Carlisle.
And if Edward was a modern man with a love of good music and good literature they would still have that in common. Bella however wouldn't probably see the apperance of Edwards 'singing' blood as a personal sign of torment. It would have been equally as difficult to control herself as it was for Edward but she would take it as proof aganst her 'character/purity/soul' like it seemed to me that it was for Edward.
Edward even as a modern man I see with more up-right morals, as if his beliefs would have carried over and he would be at odds with popular culture. Perhaps even a active church goer. He would however be more self assured, even a little bit more then modern Bella. This would change the courtship a bit.
Wiether or not years of immortal beauty, non-clumbsyness and perfect recall would have made Bella more confident I couldn't tell you.
So maybe Edward would have to ask vamp Bella out on a date.
The creation Rosalie would have ended differently as she would never have been bitter about Bella not lusting over her. Rosalie and Bella's relationship would have started out perhap more like two souls that meet tragic ends but Bella would try to help Rosalie adjust and try to see the possibilities of this new life (where as Edward most likely did not). They would be sisters.
These are just some ideas of course, I look foward to hearing what other people are throwing out there, this is really something I never thought of, very cool idea.
whee