The sentence, "I envy your new bag," is correct. It's more common to use "envy" with a person, for example: "Bob has a really fun job - I envy him!" But it's okay to use it with an object, too, for example: "I envy your job, Bob."
It can get a little confusing as well because "envy" is also a noun. For example, you could say: "Bob's job is the envy of his friends." Which means that Bob's friends all wish they had Bob's job.
It's a little complex, but I hope this helps!