He still lives with his ex

I’m starting to like someone I agreed to be fwb with. I haven’t slept with him yet even though he keeps asking me to come over. He still lives with his ex and they still sleep in the same bed but at different times supposedly. She works days and he works nights. He doesn’t seem like the type to lie to me about anything because it wouldn’t make a difference in our friendship. I just feel it’ll be disrespectful to sleep with him in a bed they both sleep in. They’ve been together for over 10 years so I don’t expect him to be over her so easily. He’s a sweetheart and I’m starting to like him a lot but idk if this is something I want to do until I know where he stands with her. Should I just trust him or wait until shes not on the lease anymore and moves out?