If you tell someone you were "carving pumpkins," you might expect them to imagine you were celebrating or observing Halloween. But if the person you were talking to lived in a country that had no Christians and did not observe the day (it is actually a North American phenomenon), they would not necessarily catch on.
The same goes for what you are reading here. The idea of "dipping" has to do with being at a Passover Seder in which foods are slightly touched or nibbled upon in an "order" (thus the Hebrew word "Seder") according to a strict liturgy.
The "bowl" and the "dipping" actually don't mean much. There is a bowl of salt water on the table. Over the centuries and (depending on which type of Jew you are or have been) certain of the Passover food item are dipped in this "bowl of tears" at certain moments during the Seder meal.
What is being emphasized in not necessarily Judas or the bowl or the dipping but the bread.
Why? Because according to Christian tradition (which oddly is not directly written in the text but only implied) Judas Isacriot does not partake of the institution of Holy Communion or what is termed the "Eucharist."
What he does receive is an anti-communion or one that induces the introduction of Satan the devil.
This is because what is being emphasized--according to Christology--is the "fulfillment" of Psalm 41:9: "Even my close friend in whom I trusted, who are of my bread, has lifted the heel against me"--even though the psalmist never says this is a prophetic forecast or is about a future messianic figure.
The language used in the Gospels is clearly chosen from Psalm 41 and from the fact that the maztah is not salted for Passover. To do so would make it impure, not kosher for a Passover Seder. (You never dip Passover bread in the bowl or add salt to it.)
The symbolism is that when one partakes of the Eucharist, one partakes of Christ. But Judas got bread dipped in saltwater, and next, as John wrote, "Satan entered into him."
These points aren't immediate since non-Jews are often reading the Gospels today. But the authors were Jewish and they were writing to Jewish Christians. Thus they often left things out because they didn't realize who else would ever be reading these texts.