Depends on how late game you are talking about. Bombards have 55 bombard strength, which is going to demolish a 40 HP city, but barely dent an 85 strength city. You might need full-blown artillery and you might want artillery corps, rather than single artillery, depending on city strength.
Leaving aside the raw firepower of your units, the key to sieges is for your units to have zone of control over every tile around the city center -- that stops city and fortification healing, so the effects of your bombardments aren't partially wiped out by the next turn's healing. Also, your war weariness is based, in part, on the number of combats your units engage in, so don't spend time taking meaningless potshots at a city that is not yet surrounded -- yes, your units build some XP when they take potshots, but, frankly, it isn't worth it, particularly if you intend to take multiple cities. Use your ranged and bombard units to clear the way for your melee units to establish ZOC around the city, and only then crash the city walls with a great concerted effort. With sufficient firepower, the city won't last 3 turns.
Note that ZOC rules are different from Civ V. Most notably, ZOC does not cross rivers, so if a city is located on a river, or intersection of a couple of rivers, you may need 3, or even 4, melee units to establish the ZOC perimeter.