Praise be to Allah.
If the fluid which is emitted is as a result of foreplay and what gets on the bedclothes is maniy (sperm) that is not mixed with any other secretions, then you do not have to wash the bedclothes because maniy is taahir (pure) according to the correct scholarly opinion.
But if what gets onto the bedclothes is madhiy (prostatic fluid) or some other secretion that comes from the private parts of the man or the woman, then you have to wash only the spot where this fluid got onto the bed, because these secretions are regarded as najis (impure).
With regard to doing ghusl, this is required in two cases:
1 – When intercourse takes place, which is when the entire glans (tip of the penis) enters the woman’s vagina, even if he does not ejaculate. In this case ghusl is required of both the man and the woman, because the Prophet (peace and blessings of Allaah be upon him) said: “When (the man) sits between the thighs and calves of a woman and the two circumcised parts touch, then ghusl is obligatory.” (Narrated by al-Bukhaari, 291; Muslim, 349). According to a report narrated by Muslim, “… even if he does not ejaculate.”
2 – When sperm is emitted without intercourse. If a man or woman reaches climax, then ghusl is obligatory. If the man reaches climax but the woman does not or vice versa, then ghusl is obligatory because of what has been emitted from them, because Allaah says (interpretation of the meaning):
“If you are in a state of Janaaba (i.e. after a sexual discharge), purify yourselves (bathe your whole body)”[al-Maa'idah 5:6]
Ghusl becomes obligatory when something is emitted or climax is reached, even if intercourse does not take place, and it becomes obligatory when intercourse takes place even if there is no ejaculation or climax, and it becomes obligatory when both take place together.
And Allaah is the Source of strength.
See Fataawa al-Lajnah al-Daa’imah; Shaykh Ibn ‘Uthaymeen, Kitaab Fataawa al-‘Ulama’ fi ‘Ushrat al-Nisa’, 36, 42; Fataawa Manaar al-Islam, 1/110.