I’m a landlord, got three shared houses, and I can’t think of a way I could stop you having bikes in the house. Even if it said no bike in the contract I can’t see how I could enforce this legally. I dare anyone to suggest how I could enforce it. As long as you were clean and there was no damage then really there is eff all anyone can do about it.
You are living in the delusion that landlords can pick and choose their tenants, this is not true. If you were clean, tidy, paid on time and were little hassle then bikes or not you would be an ideal tenant. People like this are bloody hard to find.
(I bet you a fiver someone on here will make me out to be a ****, just cos I’m a landlord, you wait and see)