Could you let me know why the 'past continuous tense' is used?
Probably because the sentence is in First Person ("I was buying"). When you have a first person sentence ("I was buying a new washer"), you can expect the sentences to be written more as if they were dialogue -- as if the character were speaking directly to you, using more informal language than a third person sentence ("He was shopping for a new washer.")
In speech, it is very common to use "buying" for the process of "shopping for," since there are not necessarily clear boundaries between "shopping for an item" and "purchasing this item." (Especially online! You click around, then you start entering in data required to purchase things; the process is not the last instant when you click the last button!)
Further, "buying" and "getting" are often synonymous in context -- "So, I was getting some bras at the department store" is easily translated to "So, I was buying some bras at the department store." This basically says that you left the store with new bras, whereas "I was shopping for some bras" means you must have more sentences to indicate whether you purchased any.
Why did your book choose to use first person? I do not know. It is possible that first person sentences looked more "interesting" to the person writing them, and they unconsciously dropped into a more informal pattern of words. It is also possible that it's a deliberate informality, to get students used to the patterns of speech so they won't be confused later when they talk to people.