Bunch is pretty safe. It is the collective term for plants (usually to the size of what you could hold in your hands) and is also used generically for any group of anything, e.g. "He pointed to the floor where there were a bunch of spanners." or "He was approached by a bunch of people playing musical instruments."
It is hard to say, generally, a bundle is (i) wrapped/secured in/by something or (ii) brought together loosely for the purposes of being carried and (in the case of plants) does not have leafy bits - e.g. A bundle of sticks; a bundle of clothes; Asparagus might work here as it usually is bound together.
Although a bunch (of flowers) may be tied together, a bunch tends to be more orderly.
When considering the distinctions, it might be useful to consider the meaning of the verbs to bunch and to bundle and the way in which they describe how things are brought together.
'Bundle' suggests items grouped loosely together, rather than neatly tied and arranged with tops at one end. A bundle of clothes/rags, twigs/branches, hay/straw, firewood. I think a 'bunch' of spanners is a slangy use of bunch, meaning 'a lot', like 'thanks a bunch'.