The mizzium apparatus allows an attuned creature to do the following:
While you are wearing the mizzium apparatus, you can use it as an arcane focus. In addition, you can attempt to cast a spell that you do not know or have prepared. The spell you choose must be on your class's spell list and of a level for which you have a spell slot, and you must provide the spell's components.
You expend a spell slot to cast the spell as normal, but before resolving it you must make an Intelligence (Arcana) check. The DC is 10 + twice the level of the spell slot you expend to cast the spell.
On a successful check, you cast the spell as normal, using your spell save DC and spellcasting ability modifier. On a failed check, you cast a different spell from the one you intended. Randomly determine the spell you cast by rolling on the table for the level of the spell slot you expended. If the slot is 6th level or higher, roll on the table for 5th-level spells.
If you try to cast a cantrip you don't know, the DC for the Intelligence (Arcana) check is 10, and on a failed check, there is no effect.
Emphasis mine. All of the spells one can roll for on the tables for a failed check have a casting time of 1 action (or longer—which still uses only your action). However, there is no stipulation that the casting time of the spell you attempt to cast must be 1 action. This leaves it unclear on how one should resolve an attempt to cast a spell with a casting time of 1 bonus action which fails. What if the caster has already used its action for the current turn? What happens if the attempted spell has a casting time of 1 reaction, like shield? Is there any reason why the item would not allow one to attempt to cast such a spell?
Note that I am looking for rules here (if any)—not rulings. An accepted answer should point to a set of rules which leads directly to its conclusions.