if a married woman claims to have committed adultery, but there is no other corroborating evidence (witnesses) is she believed by beit din such that the husband is now forbidden to sleep with her?
If there is no outside reason to believe her (eg witnesses), we do not believe her.
Shulchan Aruch, Even HaEzer 115:6:
אֵין עֵדִים שֶׁזִּנְּתָה, אֶלָּא שֶׁהִיא אוֹמֶרֶת שֶׁזִּנְּתָה, אֵין חוֹשְׁשִׁין לְדָבָר זֶה לְאָסְרָהּ, דְּשֶׁמָּא עֵינֶיהָ נָתְנָה בְּאַחֵר, וְדַוְקָא שֶׁאֵין רַגְלַיִם לַדָּבָר, אֲבָל אִם יֵשׁ רַגְלַיִם לַדָּבָר נֶאֱמֶנֶת (פִּסְקֵי מהרא''י סִימָן רכ''ב
If there are no witnesses that she committed adultery, but rather she herself says she has committed adultery, we are not concerned about this matter to forbid her [from her husband], as perhaps she [merely] set her eyes upon another. (Rema: This is only if there is no reason to believe her, but if there is reason to believe her, she is trusted (Decisions of Mahara"i #222)).