Bargaining is a completely normal, expected part of shopping in markets, bazaars, and with independent vendors — initial prices quoted to tourists are often set with negotiation in mind, so it's a standard part of the transaction rather than something to feel awkward about.
How it actually works
A friendly, relaxed approach works best — starting well below the asking price and meeting somewhere in the middle is the general pattern, and walking away is a normal, low-pressure move that sometimes brings the price down further on its own.
Fixed-price shops, larger stores, hotel gift shops, and anything with a printed price tag generally aren't open to bargaining in the same way, so reading the setting matters more than applying one approach everywhere — accepting offered tea during a visit, discussed in What Should You Know About Egyptian Customs Before You Visit?, doesn't create any obligation to buy either way.