The whole idea of a shower that you bring a festively wrapped gift in exchange for the hosts giving you food, drink, and fun. Traditionally shower gifts were household items or perhaps "for the honeymoon" personal items like lingerie and bubble bath. The hosts of the shower will likely be more than happy to suggest suitable gifts.
When one attends a wedding celebration, just like when one attends any other large dinner or party, what one OWES the hosts is a hand written letter or note of thanks. (In the case of wedding thank yous, include congratulations and best wishes for the couple.) And just like any other dinner or party, guests MAY send a gift along with or instead of the handwritten message of thanks.
It's almost always best to send a gift either before the wedding or after the honeymoon. Wedding hosts are already very busy, so don't burden with them with the tasks of accepting gifts, keeping track of who gave which, securing gifts from damage and theft, schlepping all that stuff to a place it can safely remain until after the honeymoon.
It's never rude to ASK the couple or others involved what sort of gift the couple might appreciate. Your spending level is either lavish, moderate, or modest depending on what you want. The $$$ amount corresponding with lavish or modest depends on your own level of wealth, not on the lavishness of the celebration. If you're a starving student then a $25 bath towel might be a lavish gift. But coming from a highly paid professional, that $25 gift would be extremely modest. There is NO SUCH THING as any "pay for your plate" rule.
Bachelorettes are not familiar territory. I'm an old granny lady and get invited to lots of weddings and showers, but not the "girls' night out." I suggest you coordinate with the hosts of the event regarding whether any exchange of gifts will be part of the festivities. It could be awkward if you arrived with a gift when others didn't, if others arrived with gifts when you didn't. Maybe tuck a small (in size) gift into pocket or handbag to produce or not produce as seems appropriate?