The website itself was already using cloudflare's CDN. So I added a simple cloudflare URL rule to redirect all requests hitting /images/XXX to the 3rd party image hosting service. Within a month our client's image hosting bill dropped from $~10k/month down to about $90/month, which I felt great about.
I did made one terrible mistake though - I forgot to tell our client about the configuration change. So cue a monday morning panicked phone call from our client when they got their bill, asking what on earth was happening that caused all their web traffic to disappear overnight. They thought (based on the bill) that their website must be broken and they were freaking out about it! Oops!