It is very simple to transfer or assign your blogspot blogger blog to some other other email account. You don't have to share your password. You need to follow the following steps:
Sign in with your blogger (blogspot) account
Click on Settings then click on Permission
Then a box will come where you need to add the email account (you can add more than one email account) to whom you want to transfer your blog.
The person will get an activation mail once he click the activation mail, you can make him Admin.
If you wish, you can only make him authors r Admin. Choice is yours.