Many people dip their bread in only honey over rosh hashanna but I was under the impression that one should dip in both salt and honey. What sources discuss either dipping in both salt then honey or only in honey?
.ומנהג אשכנז מטבילין פרוסת הבציעה בדבש
The custom in Ashkenaz is to dip the piece of bread into honey.
Note that he makes no mention of dipping into salt in addition to the honey.
[As noted by DoubleAA in a comment, it's possible that these sources don't mean to exclude dipping in salt as well, and are simply noting the custom to dip into honey in addition to what is normally done.]
However, as you noted in your question, some authorities do recommend dipping in salt as well:
ואחר פריסת המוציא מטבל הפרוסה ההיא של המוציא במלח ג"פ ... ואח"כ מטבלם בדבש או בסוקר לסי' טוב ואוכל.
After he says hamotzi he dips the piece of bread in salt three times ... and afterwards he dips them in honey or sugar as a good omen and eats.
Ta'amei HaMinhagim (in a footnote on p.310) records a custom to first dip a piece of bread into salt and eat, and then to dip it into honey and recite a yehi ratzon.
R. Yehoshua Mondshine in Otzrot Minhagei Chabad paras. 131-134 notes a slew of chassidic sources discussing a custom to dip in both honey and salt, but does infer (in para. 133) that the Chabad custom (at least at the time of R. Yosef Yitzchak Schneersohn) was only to use honey, and not even to have salt on the table.