I have a UBS account, I've never noticed any additional billing for the e-bills.

I regularly pay all my bills for the forthcoming month through e-financing by the beginning of said month, irrespective of when they are actually due. Once I log in, the PF interface informs me of any pending e-bills and all I have to do is click to pay them. The rest I enter manually.

Big fan of e-bills here, I wish I could use them for everything. I get an email when one becomes due, so I don't even have to remember to log on and check my online banking. Works great.

More info:
http://www.e-rechnung.ch/index_en,13862.html