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For egress, you can use bandwidth and police together.
For ingress, assuming you cannot manage other side's egress, you police other traffic to leave your 1 Mbps for video (you can also police your ingress video too).
For example, if the ingress was 10 Mbps, your ingress policy could be:
policy-map
class video
police 1024000
class class-default
police 9216000
The above is the concept, for an actual working implementation, as I believe most Cisco shapers/policers don't allow for L2, you'll need to reduce both values by about 5 to 15%. Unfortunately, percentage overhead varies per packet size so you could use worst case percentage, which is pretty large, or average case percentage.
Also, ingress traffic can burst or run above these values on the link itself. For example, video could send 2 Mbps down the link, and although it's policed at 1 Mbps, it's using 2 Mbps. TCP traffic might burst above the 9 Mbps. What might help, is if the traffic responds (i.e. slows) when there's drops, you set the policed value even lower to keep the busting below your logical limit. For example, you might physically police class default at 7 Mbps to try to avoid it bursting beyond 9 Mbps.
My experience has been traffic can often burst way above your policed limit so often you have to set a surprisingly low physical limit which unfortunately also limits your average utilization.
This is why I've previously noted, ingress traffic bandwidth management is best done on the other side's egress.
