Yeah, bicarbonate isn't doing anything for flavor like other minerals do. It's just something to overcome (or in some cases add) to get the pH right, so you can pretty much ignore it in the profile as long as the pH is right. You can just add the acid, and all the minerals, to the strike water, and you're done.
(If you were sparging Bru'n Water would have you split the minerals. If you set the mash volume for your no sparge total and sparge volume to zero, all the amounts will be right in the mash adjustment.)
EDIT Wait, you said you're starting with distilled water? Just don't add any bicarbonate. Then see if you need acid. You can get sodium, if you want it for flavor in the profile, from canning salt.