My inclination is that there would still be some concern even if the person is bedridden. How that pragmatically plays out nowadays for professionals is something to ask your local Orthodox rabbi.
Consider that yichud (with an unmarried woman) was an expansion decree of King David and his court after the rape of Tamar. Sanhedrin 21a:
(שמואל ב יג, יט) ותקח תמר אפר על ראשה (ואת כתונת) הפסים אשר עליה קרעה תנא משמיה דר' יהושע בן קרחה גדר גדול גדרה תמר באותה שעה אמרו לבנות מלכים כך לבנות הדיוטות על אחת כמה וכמה אם לצנועות כך לפרוצות על אחת כמה וכמה אמר רב יהודה אמר רב באותה שעה גזרו על הייחוד ועל הפנויה
The verse relates that after Amnon raped her: “And Tamar put ashes on her head and rent her garment of many colors that was on her” (II Samuel 13:19). The Sages taught in the name of Rabbi Yehoshua ben Korḥa: Tamar established a great fence at that time by way of her public outcry, as people said: If such an occurrence could happen to the daughters of kings, all the more so could it happen to the daughters of ordinary people. If such an occurrence could happen to modest women like Tamar, who resisted, all the more so could it happen to licentious women. Rav Yehuda says that Rav says: At that time they decreed about seclusion, that a man should not be secluded with women who are forbidden to him, and about a single woman.
יחוד דאורייתא הוא דאמר ר' יוחנן משום ר' שמעון בן יהוצדק רמז לייחוד מן התורה מניין שנאמר (דברים יג, ז) כי יסיתך אחיך בן אמך וכי בן אם מסית בן אב אינו מסית אלא לומר לך בן מתייחד עם אמו ואין אחר מתייחד עם כל עריות שבתורה
The Gemara objects: Seclusion with a woman forbidden by familial ties is prohibited by Torah law, and was not a rabbinic decree issued in the time of David. As Rabbi Yoḥanan says in the name of Rabbi Shimon ben Yehotzadak: From where is there an allusion to the halakha that seclusion is forbidden by Torah law? As it is stated: “If your brother, the son of your mother, entices you” (Deuteronomy 13:7). One can ask: But does the son of a mother entice, and does the son of a father not entice? Why mention only the son of a mother? Rather, this verse serves to tell you that only a son may be secluded with his mother. Sons are frequently with their mother, and two half-brothers of one mother consequently have the opportunity to grow close to one another. But another individual may not be secluded with those with whom relations are forbidden by the Torah, including a stepmother. Therefore, half-brothers of one father spend less time together.
אלא אימא גזרו על ייחוד דפנויה
Since seclusion, then, is prohibited by Torah law, how did Rav say that it was prohibited by a decree issued in King David’s time? Rather, say that they decreed against seclusion of a man with a single woman, to prevent occurrences like that of Amnon and Tamar.
Now, the very incident of Amnon and Tamar involved Amnon being bedridden, even though he was faking it. II Shmuel 13:
וַיֹּ֚אמֶר לוֹ֙ יְה֣וֹנָדָ֔ב שְׁכַ֥ב עַל־מִשְׁכָּבְךָ֖ וְהִתְחָ֑ל וּבָ֧א אָבִ֣יךָ לִרְאוֹתֶ֗ךָ וְאָמַרְתָּ֣ אֵלָ֡יו תָּ֣בֹא נָא֩ תָמָ֨ר אֲחוֹתִ֜י וְתַבְרֵ֣נִי לֶ֗חֶם וְעָשְׂתָ֚ה לְעֵינַי֙ אֶת־הַבִּרְיָ֔ה לְמַ֙עַן֙ אֲשֶׁ֣ר אֶרְאֶ֔ה וְאָכַלְתִּ֖י מִיָּדָֽהּ:
And Jonadab said to him: "Lie down on your bed and feign sickness, and when your father comes to see you, say to him: "Let my sister Tamar come now, and let her give me bread to eat, and prepare the food before my eyes, that I may see and eat from her hand."
To carve out exemptions from yichud restrictions for bedridden people would be counter-intuitive, as the decree wouldn't have prevented the very incident which prompted it.
See this source which claims that it does apply for sick people, and how to navigate such circumstances. See also this article about Yichud and the Physician, explaining room for leniency.