You can do this, but best to avoid thinking of it as “binding” since that is the term used for setting the “this” value. Perhaps think of it as “wrapping” the arguments into a function?
What you do is create a function that has the desired arguments built into it via closures:
var withWrappedArguments = function(arg1, arg2)
{
return function() { ... do your stuff with arg1 and arg2 ... };
}(actualArg1Value, actualArg2Value);
Hope I got the syntax right there. What it does is create a function called withWrappedArguments() (to be pedantic it is an anonymous function assigned to the variable) that you can call any time any where and will always act with actualArg1Value and actualArg2Value, and anything else you want to put in there. You can also have it accept further arguments at the time of the call if you want. The secret is the parentheses after the final closing brace. These cause the outer function to be immediately executed, with the passed values, and to generate the inner function that can be called later. The passed values are then frozen at the time the function is generated.
This is effectively what bind does, but this way it is explicit that the wrapped arguments are simply closures on local variables, and there is no need to change the behaviour of this.