Apache asks the password for every subdomain with htpasswd.

I would like he would request the password in the first input and appreciated me for those subdomains

I personally use the next code:

AuthType Basic
AuthName "Projects"
AuthUserFile /blablabla/baz.htpasswd
Require valid-user

Really Apache httpd requests your user qualifications on every request on every subdomain. It is your internet browser, which caches your qualifications (per hostname) and transmits them on every subsequent request on a single hostname.

You will never circumvent that behavior without full treatments for your clients' software if you wish to keep your different subdomains.