Bolzano has a great variety of supermarkets, so wherever you live you will have at least one shop close to your hostel. The supermarket chains that I've seen during my stay are LD, Despar, Eurospin, Billa, Polly and Metro. You can see them on the map.
I won't tell anything about the services and customer care, because they are great everywhere in Bolzano. I will pay attention on what is more interesting to the students - prices.
LD
LD (with blue color on the map) is the second biggest chain in Bolzano and has one of the most competitive prices for products like fruits, vegetables, milk and milk products, salamis, eggs etc. Like many big markets, they produce their own product line, which reduces prices even more. They have a bit higher prices of meat, but you could find something reasonable when there is a promotion.
Their supermarkets are relatively small, especially compared to the other chains. It is pretty common to see long queues on the cash desks, because they have two or three cash desks per market. Furthermore it is pretty often to see only one working cash desk. I don't know why. Maybe a politic of the market.
Working hours: Monday - Saturday 8:30 - 19:30
Despar
Despar is the biggest supermarket chain in Bolzano. They have markets in every part of the city. Maybe they offer the best quality of products, but their prices are not so low. They have their own product line, but the prices of this products are not less than their analogues in Despar and in the other supermarket chains in Bolzano.
There is one difference with that I've said in the last paragraph - there are some products , which have cheapest analogue, not only in Despar, but in the whole Bolzano. They put it at the stand's bottom most place. The brand is called Budget. You will recognize it easily by the green color of their packages. So if you go to Despar and want something really cheap, look beyond :).
Working hours: Monday - Saturday 8:30 - 19:30
Eurospin
The only Eurospin's supermarket in Bolzano is located near the train station as you can see on the map (with green color). The market is big and there is a great variety of products. They have lots of promotions, and I think this is the cheapest supermarket in Bolzano. Unfortunately it was too far from my hostel, but it deserves it to go there even once per month (for the most important products), especially when they have good promotions. You can see the promotions on their website or can download a flyer as a pdf. The website has an english version as well.
Eurospin offers very good prices of meat, and often offers attractive promotions of their meat products.
Working hours: Monday - Saturday 8:30 - 19:00
Billa
There is only one supermarket of Billa in Bolzano (marked with yellow color on the map). I've been there a couple of times. They have cheap prices only on the products of their product line, but I didn't like the prices of the other products. The quality of the stokes is good. They had remarkably good promotions of meat but that happened only 3 or 4 times during my 5 months' stay.
Working hours: Monday - Saturday 8:30 - 19:30
Polly
I've been to Polly only once. It is almost the same as LD, but with a bit higher prices. This was their only market that I've seen in Bolzano. You can see it on the map in light blue color.
Working hours: Monday - Saturday 8:30 - 19:30
Metro
I've never been to Metro. I've seen it once, while I was cycling, that's why I can't tell you anything about prices. Maybe it is reasonable to go there if you have car and you want to buy more products at once. It is in violet on the map.
At the end I will put two rank lists, in which I estimate the above mentioned supermarkets (I exclude Metro in this rank lists):
Rank list by price (from cheapest to most expensive):
1. Eurospin
2. LD
3. Polly
4. Despar
Rank list by quality of the products (from best to worst):
1. Despar
2. Eurospin
3. Polly
4. LD