I suspect Jesus was talking about the periods of time when He was in the grave and after His ascension but before the day of Pentecost. This is because He said there is no need to fast when the bridegroom is present.
Fasting is to deny the flesh and adore the HolySpirit. Once the HolySpirit was poured out there is little mention of fasting except by Paul about himself.
Since we have the HolySpirit (who is the Spirit of the bridegroom) we need only to spend time with Him in prayer and meditation. That time must often be taken from work, play and other activities of indulgence.