This "bag" was presumably the equivalent of the small box such as might store and protect the reeds/mouthpieces used by musicians in their wind instruments.
This he said, not that he cared for the poor; but because he was a thief, and had the bag, and bare what was put therein. -- John 12:6
For some of them thought, because Judas had the bag, that Jesus had said unto him, Buy those things that we have need of against the feast; or, that he should give something to the poor. -- John 13:29
Otherwise in the Synoptics we have references to the personal belt, which was hollow and could store money (Mt. 10:9, Mk. 6:8), personal money bags for coins (Lk. 10:4, 12:33ff.) and provision sacks in which to carry a variety of travel supplies, generally understood, analogous to backpacks or saddlebags (Mt. 10:10, Mk. 6:8, Lk. 9:3, 10:4, 22:35f.). All these feature in Jesus' missionary instructions to his disciples where we learn that they are to carry no money and no supplies whatsoever. This is in keeping generally with the call to discipleship in the first place, to say goodbye to one's possessions and follow Jesus.
Presumably, however, Jesus and the Twelve, being thus poor and preaching poverty, were recipients of charity, and it had to be someone's job to thus be the banker. But such money as there was can't have gone very far and did not amount to very much.
The story of the miraculous feeding of the 5,000 provides a ceiling limit for what Jesus and the Twelve might have imagined to be a lot of money. In it the disciples express incredulity at Jesus' expectation that they come up with the cash to feed so many, knowing as he must have that coming up with such a sum was pure fantasy.
He answered and said unto them, Give ye them to eat. And they say unto him, Shall we go and buy two hundred pennyworth of bread, and give them to eat? -- Mark 6:37
The penny here is the denarius, in Matthew 20 famously considered fair pay for a full day's labor or for even much less than a day's labor, which seems rather over generous (see below).
The parallel in John 6:7 indicates that 200 denarii would allow 5,000 to eat only a little and not be satisfied:
Philip answered him, Two hundred pennyworth of bread is not sufficient for them, that every one of them may take a little.
It should be stated that not even a Roman soldier would have this kind of walking around money.
At the time of Jesus, a Roman legionary received base pay of about 0.6 denarius per day (10 asses), from which the soldier had to provide for his own arms and food. That's 224 denarii per year, from the time of Julius Caesar. So try to imagine that sum in the bag Judas had, and it is not at all credible.
A soldier received other intermittent pay, boosting the base pay on average to as much as 1 denarius a day, and of course out on the perimeters of the Empire he had a reputation for intimidating the locals for additional gain, which would make sense in Palestine given the poor agricultural conditions which drove up the price of daily bread.
And the soldiers likewise demanded of him [John the Baptist], saying, And what shall we do? And he said unto them, Do violence to no man, neither accuse any falsely; and be content with your wages. -- Luke 3:14
Content with your wages. Theoretically, the cost of a one pound to one and half pound loaf of bread at this time could be as high as 2 asses or as little as 1, but double this on the poor soil of Palestine. So 200 denarii would feed at the outside 1,600, or as few as 800, with say 1,400 calories each. The conundrum with even 200 denarii means the 5,000 would have to get by on 224 to 448 calories each. While the problem in the story sounds about correctly imagined, the prospect of the availability for purchase of such a great quantity of bread as well as of solving the logistical and distributional problems implied seems as utterly fanciful as the notion that they might have had the means to purchase so much bread in the first place.
On the other end of the scale it makes sense that the bag which Judas had could often be quite empty, necessitating scrounging operations on the part of Jesus and the Twelve themselves just to survive.
At that time Jesus went on the sabbath day through the corn; and his disciples were an hungred, and began to pluck the ears of corn, and to eat. -- Matthew 12:1
And it came to pass, that he went through the corn fields on the sabbath day; and his disciples began, as they went, to pluck the ears of corn. -- Mark 2:23
And it came to pass on the second sabbath after the first, that he went through the corn fields; and his disciples plucked the ears of corn, and did eat, rubbing them in their hands. -- Luke 6:1
The needs of Jesus and the Twelve at a minimum subsistence level of 1,400 calories daily would mean in the hardest of times requiring as much as 3.25 denarii a day (4 asses for one loaf of bread X 13 = 52 / 16). Charity must have played an outsized role in the ministry of Jesus and his disciples.
Hence the centrality of daily bread to the Lord's Prayer, and the fame and survival of the bread sayings generally throughout the Gospels.
Therefore I say unto you, Take no thought for your life, what ye shall eat, or what ye shall drink; nor yet for your body, what ye shall put on. Is not the life more than meat, and the body than raiment? -- Mt. 6:25
Therefore I say unto you, Take no thought for your life, what ye shall eat, or what ye shall drink; nor yet for your body, what ye shall put on. Is not the life more than meat, and the body than raiment? -- Mt. 6:25