You said it yourself, witch bolt "ends if you use your action to do anything else". Using your bonus action isn't using your action.
In 5e, it's just "action" not "standard" action, and as you also said "movement" actions aren't a thing. PH 189 says that "On your turn, you can move a distance up to your speed and take one action."
If you spend that one action doing not-witch bolt, the spell ends. Anything else you do with your move, bonus action, or reaction are immaterial—unless those actions violate one of the restrictions of the spell you already listed (like using your bonus action to misty step out of line of sight).
If you don't spend your action casting the spell, you have stopped casting the spell
There are only a couple of possibilities for what could happen if you start casting a spell with a long casting time and then don't use your action to continue casting it:
- The casting continues uninterrupted, and this round counts towards the casting time.
- The casting is paused, so this round doesn't count towards the casting time, but you can resume casting next round as long as you maintain concentration.
- The casting is cancelled, and you would have to start over from the beginning if you still want to cast it.
I can't think of any other reasonable interpretations of the rule besides these 3.
Option 1 is directly and unambiguously at odds with the rules, which say that "you must spend your action each turn casting the spell". So we can eliminate it right away.
Option 2 seems plausible, but there are a lot of problems you need to address if you use this interpretation. For example, how many rounds in a row can you "pause" the casting before the spell is lost? Could you pause casting a spell 1 round before you finish, and then wait indefinitely for the opportune time to complete it, thereby allowing you to set a trap with a spell that normally has a prohibitively long casting time? In short, Option 2 implies a whole new set of possible mechanics relating to "paused spellcasting" and its interactions with other mechanics, none of which are addressed at all in the rules. That makes it very unlikely that this is the intended reading.
So, having eliminated those two options, the only reasonable interpretation left is Option 3: the spell's casting is cancelled. This is certainly the most literal reading of the rule: if you spend your action each turn casting the spell, you cast the spell; if you don't spend your action each turn casting the spell, you don't cast the spell. The rules don't say that the spell fails if you don't use your action to cast the spell, because they don't need to. The spell doesn't fail: you simply don't cast it because you stopped casting it. The requirement to maintain concentration through the full casting time is an additional requirement to cast the spell and is unrelated to the requirement to spend your action each turn casting it.
(I agree that this logic gives an absurd result when combined with the rule that a surprised creature cannot take an action on the first turn of combat, but I would argue that the fault lies with the surprise rules, not the spellcasting rules.)
Best Answer
You have to concentrate to maintain the spell, and spend your action each turn casting the spell
Longer casting times are noted in the PHB and Basic rules. I'll quote the relevant text from D&D beyond (the official 5e web toolset), since it is the easiest source to search online.
You are still free to use your bonus action and reaction as appropriate
None of the rules for longer casting times here directly prevent you from using an available bonus action, reaction, or movement on your turn. So, you may use them as appropriate on your turn without your spell failing.
Using movement doesn't take an action, so you can still move and cast the spell
As noted in the PHB, basic rules, and D&D Beyond:
Moving on your turn doesn't take an action, and it doesn't break concentration. So unless the spell or some other effect requires you to stand still, you can still move on your turn.
You are limited as to casting spell with your bonus action though:
As noted in the rules on bonus action spells:
Considering that you must continue to use your action each turn to cast the original spell, unless that spell is a cantrip, you wouldn't be able to cast a bonus action spell in the same turn. Luckily, spells that require your reaction don't have any such limits, so you can use those as often as you are able.