E.W.
As a recent bride, I would suggest either throwing a shower from your side of the family, or asking the bride's side of the family if you could join their shower.
If you don't do anything, it will make the bride feel as though (a) she isn't welcomed into the family, (b) you don't care about her, and/or (c) you're too cheap to give them anything.
EDITED TO ADD: T., I was not trying to imply that you are any of the above things, it's just that with this type of event, someone could take things the wrong way if something isn't handled properly. For our wedding, my mom threw the bridal shower at her home and invited everyone on my husband's side of the family since his family is very small and it wouldn't have made sense for them to throw one of their own. Since this was the case, his mother asked what she could contribute to the event (so that there was effort from his side of the family). I was hurt, though, a few months later by some friends of mine who threw a bridal shower for a mutual friend of ours, but they didn't even think to throw one for me. This is what I was trying to convey.