Imagine that Bob John and Jill are walking down the street and they come across a dead body.

Bob says" let's call for help!"


Jill calls the police and nothing eventful happens.

Is there something wrong with the grammar of Bob's exclamation?

He said "us" yet only Jill actually engaged in the action of getting help.

I feel like I'm on the something weird here so I've tried to find some more sentences like this

More generally, this relates to groups performing collective actions:

"We called for help." (As in your situation.)
"We drove here as a family." (But not everyone drove, perhaps just the parents or one parent.)

"Drive" is an especially interesting verb in this case, because it can even be extended to singular usage for passengers. "How did you get here?" -- "I drove.", even if actually it wasn't "I" who drove but a friend, while I rode in the car. The collective action of "driving" though applies to the whole group. Note that it does not apply when riding the bus, even though there is a driver there, but not part of the relevant group. I suppose in some sense this relates to responsibility, similar to how someone in the workplace might be reprimanded for not doing a task but (probably) only if someone else (e.g., on their team) didn't already do it. "You should have done it!" -- also interesting that in English, "you" is ambiguous between singular and plural, and I think in some cases that fits this type of discourse well, although I'm not sure how that works out in other languages.

Collectivity and related semantic concepts are complicated for linguistic analysis and in some ways just beginning to be explored in linguistic theory (at least compared to other topics). Even just plurals in general are a more complex topic than singulars, when for example thinking about the sort of referents that noun phrases express: we think about entities as subjects ("Who drove?" / "John drove."), but in fact once we consider data from plurals we must consider sets of entities rather than just individuals, and everything gets much more complicated. (There's also a question of whether singulars are sets of single individuals, or if there is actually a substantive distinction between singulars as individuals and plurals as sets!) See, for example, Lasersohn (1995), Plurality, Conjunction and Events: https://www.springer.com/us/book/9780792332381

As panini points out, "let's" often has this collective sense, but it's by no means a grammatical anomaly, no more than other collective/plural/etc. usage in general.