You can often buy a bunch of flowers at the local supermarket, or gas service station (in the UK). It's a collection of different flowers grouped together - or sometimes the same flower especially in the case of red roses 😉
If I wanted to get a 'bouquet' of flowers, I would go to the local florist, who would spend some time putting together an artistically organised collection of flowers, which would be be firmly attached together, in order to maintain their pleasing aesthetic appearance.
Bouquets can be large or small and are often associated with weddings funerals or special anniversaries.
The bride at a wedding often carries a small bouquet that she will throw behind her, after the marriage, to be caught by someone. Tradition has it that the person catching the bouquet will soon be getting married themselves. (again, in the UK - but probably another English speaking countries too...)
Bouquets usually cost a lot more than 'bunches' too. 😯