It depends how you define bandwidth.
Using the 2.4 band as a example you have 3 usable channel groups. 1,6,11 So you have let say 150m per channel...kinda a lie...
The cheap repeater only has a single radio so it can only run on a single channel. Let say 1. So you are dividing 150m in half and the other 2 channels 6 and 11 are not used for anything ...well your neighbors may use them.
Now if you use a bridge and a AP and you place them on the same channel there is no advantage; but because there are 2 radios now you can place the bridge on channel 1 and the AP on channel 6. You now have a total bandwidth of 300m but you still have to send the same signal twice, ie the bridge to the router and the AP to the client. So from client to router your effective rate is cut to 150m.
So technically you are still cutting the bandwidth in half but you are using more to start with.