How to filter aggregation pipeline by specific ids

Question

Given this data:

{
  "_id": 1,
  "name": "jim",
},
{
  "_id": 2,
  "name": "bob",
},
{
  "_id": 3,
  "name": "bill",
},
{
  "_id": 4,
  "name": "bob",
}

I have a simple aggregation pipeline to retrieve documents with the name bob:

[
    { "$match": { "name": "bob" } }
]

However, I also have an array of ids (e.g. [1, 2]) that I want to use to filter the documents (either before or after the $match query runs). So the final result of the above aggregation pipeline should be:

{
  "_id": 2,
  "name": "bob",
}

Usually I would do this with a query like { "_id": { "$in": [1, 2] } }, however having been through the MongoDB docs it appears the aggregation operations are different from regular aggregation operations, and I can't seem to find an aggregate that can achieve this (neither in the docs nor online).