The Aruch Hashulchan paskens that the mitzva of Bikkur Cholim also applies to a man visiting a woman and a woman visiting a man. The Tzitz Eliezer wonders where the Aruch Hashulchan derived this halacha from and disputes him. He says: Man to man. Woman to woman.
My two cents [with the disclaimer that the Aruch Hashulchan was one of the poskei ha-dor in his time and the Tzitz Eliezer was one of the biggest poskim of our times and I am less than a nothing-nobody so my opinion is just a suggestion made as food for thought]: We have two conflicting values at play - Tzniyus and the mitzva of bringing respite to the great pain of ill people. So the will of Hashem regarding visiting members of the opposite gender may be nuanced and not a yes or no proposition. If one is going around the hospital visiting patients for two minutes each, offering a smile and some kind words and a tefillah for refuah then why shouldn't the opposite gender receive the same attention? If one is with a group then it also makes sense that everybody should be visited.
However, spending long periods of time alone talking with a member of the opposite gender should be discouraged.
Also, many patients wouldn't feel comfortable with a member of the opposite gender visiting them such as Chasidim who are very strict about limiting inter-gender contact on any level. So that should be avoided.
Besides the mitzva of Bikkur Cholim it is also a great Kiddush Hashem when religious people visit random people in hospitals.
יהא חלקי עמהם!!!
