The easiest and most convenient way from the North side (Russia) goes from the Kurush village and takes two days of quite intensive hiking. There are no marked trail nor visible tourist activity so you can enjoy the virgin condition of the mountain - please, leave the place in the same state as you find it - absolutely clear from the human garbage! Also there is no infrastructure, no rescue service in the area, plenty of wildlife including bears (you should be careful leaving your stores unwatched).
Bazarduzu also can be climbed from Azerbajan side, but due to the complicated transport access and lots of the climbing formalities to be regulated with the National Park, access from Russia is easier (but also some paperwork required)
4x4 drive from Derbent via E50/E119/P-217 takes 4-5 hours and when the road ends you can camp below Kurush village or find some accommodation facilities in the village - the inhabitants are extremely friendly.
You cross the river Chekhichay by the bridge in the narrow gorge and keep right until you reach the smaller river. Follow the cows tracks by the left bank until the possible crossing point and get to the right (as you facing the mountain) bank of that river. Further you follow slight trail mostly uphill and in 2.5-3 hour you reach first good camping site at the level of 2600 m. If you feel well it is better to continue up as from the first camp it is a very long way to the summit. In one hour from the camp you reach a deep canyon which is to be crossed a bit higher on your right (some scrambling is possible while getting to the opposite side of the canyon). Then continue going up keeping to the right side of the huge scree slope. When at the level 3100-3200 cross the slope to the left and you are on the good camping spot from which the summit can be reached in 4-6 hours. Late in the season there could be a problem finding water there. From the camp you go to the base of the West slope of Bazarduzu 3800 and turning left climb towards the summit following the wide and comparably easy scree slope until the top.
For the climb of Mount Bazarduzu early in the season it is recommended to have all the set of alpine clothes, crampons, light ice axe and crampons.