Who Typically Hosts the Shower?
One or more of the bridesmaids, usually led by the Maid or Matron of Honor, are the most typical hosts of the wedding shower, although just about any close friend, neighbor, aunt, cousin, or coworker is perfectly fine, too. You can cohost it if you want with any of these people, or you can do it by yourself.
Who Should NOT Host the Shower?
The people who are not supposed to host the shower, according to the etiquette bylaws, are the mother, sister, or grandmother of the bride. However, any of these can hold it at her home, or offer financial contributions to the event. She just is not typically supposed to act as hostess (she doesn't send out the invitations).
She's Got a Bunch of People Who Will Want to Throw Her a Shower
What with work friends and friends from the bride's club, church, school, old family friends, or any one of many disparate groups in a woman's life, chances are there will be plenty of people who want to throw a shower. Probably lots of them don't even know one another. Who's the right one to do it, and how many showers can she have?
That question is answered in many ways. First, are the bride and groom having a big wedding? Are all the people who will be at the shower(s) also invited to the wedding? Is she inviting her whole office staff to the wedding, or just a few people from work?
People who are not invited to the wedding can certainly be invited to a shower. But some wedding-planning books advise the bride not to have shower guests who are not also wedding guests.
Remember that it is redundant and possibly a big financial drain on anyone to be invited to more than two showers for the same bride. With that in mind, it can also make a shower a lot more fun for the bride if groups of people she knows from different parts of her world can meet. Her best friend at work can finally meet Aunt Mabel, about whom she has heard so many stories. It's a kick for some brides to watch this. On the other hand, coworkers might not feel generally comfortable at the family get-together, or their presence there might establish more intimacy with the bride than she feels comfortable with.
For the hostess of the party, the easiest way to resolve this is to ask the bride what she wants. As long as one or two poor souls don't get invited to more than two showers for the same bride, everything will work out just fine. And some of the bride's friends might make new friends with other people who are important in her life.

