Ich hole frische Brötchen im Supermarkt.

Holen literally means “to fetch” or “to pick up.” It emphasizes that you go somewhere and bring something back.
• kaufen = to buy (focus on the purchase)
• bekommen = to receive (focus on being given)
In this sentence, you’re stressing that you’re going to the supermarket and getting fresh rolls yourself.

In German, there is no indefinite article in the plural. If you’re talking about rolls in general (not “the rolls” or “a pair of rolls”), you simply say frische Brötchen.
If you wanted to specify a quantity you could say:
• ein paar frische Brötchen (a couple of fresh rolls)
• drei frische Brötchen (three fresh rolls)

Because you’re using strong adjective declension:
• No article (strong declension) + plural noun in the nominative case ⇒ adjective ending -e.
Pattern:
• Single fresh apple: frischer Apfel
• Fresh apples (pl.): frische Äpfel (or frische Brötchen here)

im is the contraction of in dem. After in you use the dative case when talking about location (where something happens).
• in dem Supermarkt ⇒ im Supermarkt (dative)
If it were movement into the store as the focus, you would use the accusative: ins Supermarkt (in das Supermarkt).

• in + dative = inside a place (here: inside the supermarket).
• bei + dative would mean “at” or “near” someone/somewhere (not inside).
Since you actually go into the supermarket to get the rolls, in is correct.