Hex and invisible are both concentration so it dies not cone up a lot.
This is true; however, I believe potions do not require the user to maintain concentration on the effects. Therefore a potion of invisibility could allow the situation.
Hex is an interesting spell. The first sentence states "You place a curse on a creature ..." This tells me two things: 1) The spell is a curse, 2) casting the spell is placing a curse. The spell description also states, "... before this spell ends, you can use a bonus action on a turn of yours to curse a new creature." The critical question that I would pick Crawford's brain about is, "Is placing a curse as a bonus action the same as placing a curse while casting a spell?" I would think his response would be along the lines of, "It would state the need to cast the spell in the text if it were intended." So, my ruling would be that an invisible caster can us their bonus action to curse another creature without casting a spell. Since invisibility states it ends with an attack or casting a spell, then invisibility would remain.
Regarding the use of an action to cast a spell from a bard instrument, I would agree with jaelis. If the magic item allows the caster to cast a spell, then the caster is casting the spell. The magic item is not casting the spell. Thus, the bonus spell cast should be limited to a cantrip. A magic item user can still activate an item for an effect as an action and still cast a spell as a bonus action.