It depends. For heart rate to lower the size of the left ventricle must increase so more blood can flow with each heart beat. You'll probably get some improvement in a few days and then it will likely taper down and you'll get what appear to be random improvements.
I have found that a stressful day is often a sign that improvement is about to occur. That doesn't mean you should stress yourself out to try and get improvement because that won't work. But if you notice you have a bad day (out of sync at work, more frustration in traffic than normal, general irritability, sleep issues) the next day or two you may make a jump forward followed by a pull back and return to a calmer wave pattern.
One tip I can give you is to always breathe through your nose when exercising, inhale and exhale. No mouth breathing!!!
Good luck to you. Don't get discouraged if improvement doesn't happen every week. It usually comes in regressions, jumps forward, and plateaus. For me aerobic exercise is medicine and I approach it that way. I take it every day and I know I will have to for the rest of my life. It's not always enjoyable, but the benefits far outweigh the effort.