Peace All
Even though toothpaste was not invented in the times of the prophet Muhammad (SAW) bad breath was. Hadith clearly acknowledges that fasting causes bad breath. We should not worry about it. I tend not to talk too much anyway while fasting and keep my distance from people when talking. I don't make apologies for bad breath.
The rinsing of the mouth for wudu is a good way to reduce the bad taste, but fasting is bound to cause bad breath because of the stomach juices.
Also, in my personal ijtehad (if you can call it that) mint flavoured (possibily alcohol containing) mouthwash or toothpase compared to siwak which does not taste of any food, is not a suitable alternative. Taste especially is linked with how our stomach functions.
If taste was no concern then we should be allowed to put mint leaves in our mouths and spit them out without swallowing too.
One possible discretion could be if some sort of toothpaste flavour was found without any food associated taste, then perhaps it could be possible. By the way I don't do ijtehad ... just wanted to clear that!
I frequently attend office meetings where the next person is sitting next to me in a chair , Should I go and stand in the corner to attend a 4 hour meeting ? I should be punished for being a practicing Muslim. Or I should take one month leave for Ramazan ?
My role also dictate that I sit in front of a computer and explain something to a user of software program who is sitting beside me , how can I accomplish this feat with offending this person with my bad breath ?
So is true for many Muslims who are in Public dealing and similar kind of situations. Islam did not come to enlighten and reward only those who can afford to maintain the distance from people during Ramazan , it is Universal Religion , its rules are applicable to each situation.
The Quran and hadees prohibits eating and drinking during fasting , there is no prohibition on tasting. Based on this some fuqaha/ Alims of Islam have allowed tasting of food by a wife who's husband is abusive and will punish her for serving bad food. I have read it somewhere and my mind accepts this taweel . If someone does not agree they have the right to differ. Again it all boils down to intentions.
Allah knows the best. (wallah ho alim).