D.E.
It's kind of rude that they sent you a invite to the Bridal Shower and you don't even live there. I thought that it was only customery to send to people who live in the area and who you think mught come. You don't send an invite to every female i and out of State just trying to get more gifts, that's rude and per greed.
I wouldn't worry about sending a gift for the Bridal Shower, if you don't live where the Bride is, don't worry about it.
If you go to the Wedding, then you can get them a Wedding Gift and if you don't make it to the Wedding, you still send them something.
I never heard of being invited to a Bridal Shower and not living in the area to go.