He could travel in space by his great mystic powers, and it is understood that he traveled a great distance through space, even up to the Vaikuntha planets beyond material space. He traveled all these long distances within one year
SB Canto 1
During our exile, Durvāsā Muni, who eats with his ten thousand disciples, intrigued with our enemies to put us in dangerous trouble. At that time He (Lord Kṛṣṇa), simply by accepting the remnants of food, saved us. By His accepting food thus, the assembly of munis, while bathing in the river, felt sumptuously fed. And all the three worlds were also satisfied.
Durvāsā Muni: A powerful mystic brāhmaṇa determined to observe the principles of religion with great vows and under strict austerities. His name is associated with many historical events, and it appears that the great mystic could be both easily satisfied and easily annoyed, like Lord Śiva. When he was satisfied, he could do tremendous good to the servitor, but if he was dissatisfied he could bring about the greatest calamity. Kumārī Kuntī, at her father's house, used to minister all kinds of services to all great brāhmaṇas, and being satisfied with her good reception Durvāsā Muni blessed her with a power to call any demigod she desired. It is understood that he was a plenary incarnation of Lord Śiva, and thus he could be either easily satisfied or annoyed. He was a great devotee of Lord Śiva, and by Lord Śiva's order he accepted the priesthood of King Śvetaketu because of the King's performance of sacrifice for one hundred years. Sometimes he used to visit the parliamentary assembly of the heavenly kingdom of Indradeva. He could travel in space by his great mystic powers, and it is understood that he traveled a great distance through space, even up to the Vaikuṇṭha planets beyond material space. He traveled all these long distances within one year, during his quarrel with King Ambarīṣa, the great devotee and Emperor of the world.
He had about ten thousand disciples, and wherever he visited and became a guest of the great kṣatriya kings, he used to be accompanied by a number of followers. Once he visited the house of Duryodhana, the enemy cousin of Mahārāja Yudhiṣṭhira. Duryodhana was intelligent enough to satisfy the brāhmaṇa by all means, and the great ṛṣi wanted to give some benediction to Duryodhana. Duryodhana knew his mystic powers, and he knew also that the mystic brāhmaṇa, if dissatisfied, could cause some havoc, and thus he designed to engage the brāhmaṇa to show his wrath upon his enemy cousins, the Pāṇḍavas. When the ṛṣi wanted to award some benediction to Duryodhana, the latter wished that he should visit the house of Mahārāja Yudhiṣṭhira, who was the eldest and chief among all his cousins. But by his request he would go to him after he had finished his meals with his Queen, Draupadī. Duryodhana knew that after Draupadī's dinner it would be impossible for Mahārāja Yudhiṣṭhira to receive such a large number of brāhmaṇa guests, and thus the ṛṣi would be annoyed and would create some trouble for his cousin Mahārāja Yudhiṣṭhira. That was the plan of Duryodhana. Durvāsā Muni agreed to this proposal, and he approached the King in exile, according to the plan of Duryodhana, after the King and Draupadī had finished their meals.
On his arrival at the door of Mahārāja Yudhiṣṭhira, he was at once well received, and the King requested him to finish his noontime religious rites in the river, for by that time the foodstuff would be prepared. Durvāsā Muni, along with his large number of disciples, went to take a bath in the river, and Mahārāja Yudhiṣṭhira was in great anxiety about the guests. As long as Draupadī had not taken her meals, food could be served to any number of guests, but the ṛṣi, by the plan of Duryodhana, reached there after Draupadī had finished her meals.
When the devotees are put into difficulty, they have an opportunity to recollect the Lord with rapt attention. So Draupadī was thinking of Lord Kṛṣṇa in that dangerous position, and the all-pervading Lord could at once know the dangerous position of His devotees. He therefore came there on the scene and asked Draupadī to give whatever food she might have in her stock. On her being so requested by the Lord, Draupadī was sorrowful because the Supreme Lord asked her for some food and she was unable to supply it at that time. She said to the Lord that the mysterious dish which she had received from the sun-god could supply any amount of food if she herself had not eaten. But on that day she had already taken her meals, and thus they were in danger. By expressing her difficulties she began to cry before the Lord as only a woman would do in such a position. The Lord, however, asked Draupadī to bring up the cooking pots to see if there was any particle of foodstuff left, and on Draupadī's doing so, the Lord found some particle of vegetable sticking to the pot. The Lord at once picked it up and ate it. After doing so, the Lord asked Draupadī to call for her guests, the company of Durvāsā.
Bhīma was sent to call them from the river. Bhīma said, "Why are you delaying, sirs? Come on, the food is ready for you." But the brāhmaṇas, because of Lord Kṛṣṇa's accepting a little particle of food, felt sumptuously fed, even while they were in the water. They thought that since Mahārāja Yudhiṣṭhira must have prepared many valuable dishes for them and since they were not hungry and could not eat, the King would feel very sorry, so it was better not to go there. Thus they decided to go away.
This incident proves that the Lord is the greatest mystic, and therefore He is known as Yogeśvara. Another instruction is that every householder must offer food to the Lord, and the result will be that everyone, even a company of guests numbering ten thousand, will be satisfied because of the Lord's being satisfied. That is the way of devotional service.