How to get to the monastery
As you drive south from Asenovgrad, you enter the Rhodope Mountains. Just two kilometres south of town is Asenova Krepost (Asen's Fortress). Then, at ten kilometres from Asenovgrad, is the monastery. A sight that shouldn't be skipped. Actually, Asenovgrad, the Fortress and Bachkovo Monastery are a standard itinerary. It's an easy combination of sights that can be packed into a day. It's a beautiful area with a good road connecting all these sights. No need to walk much from the car parking but should you fancy a hike, there's endless opportunities.
Once at the parking, just walk with the crowds. There's many souvenirs in the alley leading upto the monastery. Before the crowded part with souvenir stalls, on your left is Restaurant Vodopada with an outside terrace. There's a waterfall and you can have a coffee right next to the pond. It's lovely. They serve fresh fish, most likely trout. This could be caught in the Chepelarska river (local people call it 'Chaja'). The bathroom of the restaurant is paid separately, no matter if you're a guest or not.
Walk up to the monastery and admire the outside, pass through the gate and just walk around leisurely. You might see a wedding going on, especially on Saturdays. Preferably, arrive early on the weekends as there are many tourists for just a day. It's possible to spend the night in the monastery. I'm not entirely sure about the visiting hours of the monastery, either way the first mass in church is at 7:00 in the morning. Then, there's one at 17:00 (18:00 in summer). So, you can arrive early and have the surroundings all to yourself.
Learn about its history
Just some information about the monastery itself; it's the second biggest monastery in Bulgaria, after the Rila Monastery. Actually, it's one of the oldest and largest Eastern Orthodox monasteries in Europe. The initially Georgian-oriented monastery was established in 1083 by Gregory Pakourianos. He was a Byzantine politician and military commander. There was a school where religion was taught to young pupils, as well as mathematics, music and history. From its foundation on, the monastery was mainly inhabited by Georgian and Chalcedonian Armenian monks. Then, during the era of the Second Bulgarian Empire, when these monks lost their patriarchy over the monastery, things changed. Later on, during the Ottoman invasion of Bulgaria, it was destroyed and then rebuilt in the 16th Century.
Unfortunately, the only structure left from before the destruction, is the Ossuary (a place where human bones are stored after being exhumed, which means the human remains are dug up and transferred to such Ossuary). Read more about this Ossuary on this Wikipedia page. The Ossuary is a bit outside the monastery complex. To learn more about Ossuaries in general, visit this page.
Inside the complex itself, the main church, named after Virgin Mary and built in 1604, features the icon of the Virgin Mary Eleusa from 1310. It comes from Georgia and attracts many pilgrims. This church was built on the exact place the former church used to stand, which was destroyed by the Ottomans. Apart from the other three churches inside the complex, there's plenty to see in the courtyard as well. There's a two-century old Diospyros lotus tree brought in from Georgia. In addition, there's the impressive scenic mural on the wall in a corner of the courtyard. It's the largest scenic mural on the Balkans and still looks surprisingly good, because of the technique the Bulgarian painter Alexi Atanasov used.
It's also a starting point for hikes
Not as old as the Rila Monastery, yet still widely-known and visited in large numbers, make sure to visit this monastery. There's several nice walking trails starting from right in front of the monastery. Interestingly, there's great nature in this area, such as the plant Haberlea Rhodopensis, unique to the Rhodope Mountains.