The rule in the PHB is fairly clear on casting a cantrip and a spell: if the spell is a bonus action, you may cast a cantrip as an action.
My question concerns the two bonus-action cantrips, magic stone and shillelagh. Can one of these spells be cast as a bonus action and then another cantrip, like fire bolt, be cast as an action?
Specifically, what the rule (PHB 202; Casting Time > Bonus Action) says is that when you have cast any spell (including cantrips) using your bonus action, you are limited to casting a cantrip using your action (i.e. not a spell of 1st level or higher).
Thus, you can cast cantrips with both your action and bonus action on the same turn.
Cantrips are spells. Therefore, unless specified otherwise, they follow all the rules that apply to spells in general. The status of cantrips as spells is often forgotten because many rules specifically refer to "spells of 1st level or higher", but unless so excluded they do count as spells. This is specified in the Basic rules (available for free on DnD Beyond):
Spell level
Every spell has a level from 0 to 9. A spell's level is a general indicator of how powerful it is, with the lowly (but still impressive) magic missile at 1st level and the earth-shaking wish at 9th. Cantrips -- simple but powerful spells that characters can cast almost by rote -- are level 0. ...
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Cantrips
A cantrip is a spell that can be cast at will, without using a spell slot and without being prepared in advance.
So the normal rule applies: if you cast any spell – cantrip or not – as a Bonus Action, you can cast another spell on the same turn only if it's a cantrip with a casting time of one Action. Fire bolt is such a cantrip, so casting it to follow after a Bonus Action spell, cantrip or otherwise, is legal.
This rule appears in Chapter 9: Spellcasting of the Basic Rules (and PHB). In the Casting Time section, it states:
Bonus Action
A spell cast with a bonus action is especially swift. 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.
In the same chapter, under Cantrips, the rules define a cantrip as:
a spell that can be cast at will, without using a spell slot and without being prepared in advance.
(Emphasis mine in both excerpts.)
When the rules specifically exclude cantrips, they use the phrase “spells of 1st level and higher” (for example in the Spellcasting class features granted to many classes). The term “spell” on its own includes both cantrips and higher level spells.
Therefore yes: if you use your Bonus Action to cast any spell with a casting time of 1 Bonus Action, including the cantrips magic stone and shillelagh, you can then use your Action in the same turn to cast a cantrip with a casting time of 1 Action.
