Can you explain why a Narrow bandwidth means that we will need more time to transmit the signal ?
Because narrow bandwidth means that the signal should change slowly (at low frequency).
You cannot change signal at a quick speed, because bandwidth is limited. Shorter rise/fall time means higher frequency components in the signal, they require wide bandwidth.
When you use narrow bandwidth filter (in order to reduce noise influence), you will needs to use low frequency signal for the carrier modulation. So, it needs more time to detect it on receiver side, just because low frequency has longer period and needs more time to detect one period.
I thought it depended only on the upper frequencies of the continuous band of frequencies and not on its width.
Absolute frequency value doesn't matter. Bandwidth matter.