There are several buslines going to Rabat, from the main busterminal in Valletta it should take about 35 mins. 53 Valletta-Rabat, 52 Valletta-Dingli through Rabat, 51 Valletta-Mtarfa through Rabat
Rabat is also only a short walk from Mdina - through regular city streets with plenty of quaint buildings and homes. Simply exit the old capital's fortress walls and keep walking; soon enough, you'll be in Rabat.
