If you find one Catholic person there, ask them if they want to see a priest. Normally, other patients will notice that a priest is present and could ask to talk to him.
This has worked in the past. One member of our local Militia Maria got a priest in a hospital to visit his dying father and asked the person in the bed next to him if he also wanted to meet the priest. The man was delighted , spent a lot of time with the priest and promptly died the following week. The priest confirmed that he was very receptive to the last sacraments
If there is a Militia Maria at your church, you could always join and find fellow enthusiasts who also collect 11th hour workers.