The query team has discussed and decided on the following syntax/semantics:

Name: $binarySize

Alternate Names: $binSize, $byteSize

This expression takes an expression that evaluates to a string or BinData and return the size of the value in bytes. It will error if the result evaluates to a type other than string, BinData, or null. Given nullish, returns null.
Syntax:

{ $binarySize: <Expression> }

This will parse like all other unary expressions, and accept the argument by itself or as an array with one element.

Original Description

Implement an aggregation expression that return the length of BinData type value.

This would work much in the same way as SERVER-14670

Examples
Input

db.coll.insert({_id: 0, bin: new BinData(3, "OEJTfmD8twzaj/LPKLIVkA==")})

Pipeline

db.coll.aggregate([{
    $project: {
        "BinLength": {$binLenBytes: "$bin"}
    }
}])

Output

{_id: 0, BinLength: 16}