Unlikely it would get air in system of was bled properly before unless the coolant level had dropped significantly.
I find when bleeding the system if you get it about there then just go for a drive the increased engine speed will usually expell any air into the expansion tank. Make sure the heater are set to hot.
So next step is to go through the fan system.
You say the car tends to overheat when idling and the fan isn't coming on..
I would check the fan works by disconnecting the fan switch which is usually on the thermostat housing.
And link the pins in the plug with a piece of wire, bypassing the fan switch.
If the fan comes on then next check the fan switch.
If fan doesn't come on when you link that plug out, then there's a fault either with the fan or wiring or fuse has gone etc etc.