According to the rules of jurisprudence, you are not required to perform ghusl after sexual intercourse if you started menstruated immediately. The reason for it is that even though you perform ghusl, being in a state of menstruation, you are still ritually impure to perform Prayer or tawaf, etc.
Having said this, you can still bathe for your satisfaction. Bathing is a good practice even while you are menstruating.
Allah Almighty knows best.
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