The rules for bonus-action spells state:
You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.
However, counterspell seems to interrupt the casting of a spell thus preventing it from completing and causing it to fail:
You attempt to interrupt a creature in the process of casting a spell. If the creature is casting a spell of 3rd level or lower, its spell fails and has no effect.
So, if indeed the spell was never completely cast, are you still restricted to casting a cantrip with a casting time of 1 action that turn?
Best Answer
RAW is unclear
Based on the language use of interrupt and spell fails and has no effect, there can easily be confusion in interpreting the final effect of a cast or uncast spell.
This question covers a lot of the discussion, especially between the two top rated answers, but we do have some clarification from Jeremy Crawford on Twitter.
Crawford Clarifies the order of events
In a tweet that covered the question linked in the paragraph above, Crawford states (emphasis mine):
It is clear Crawford believes a spell that has been counterspelled is still cast.
If cast, then regular spellcasting restrictions persist
If you have used your Bonus Action to cast a non-cantrip spell, then you can only cast a cantrip with your Cast a Spell action.