First of all, great question. This difference for a seemingly related word of measurement hadn't even entered my mind until you asked about it, but reading your post made me want to look into it. Before I go any further, I want you to know that I found nothing that definitively answered the "why" to your question. However, I did come across some information that I hope is interesting to you and others who read this post.
The first thing I did was search Google to see if I could find any instance of "bazı" with the singular. Though not as numerous as with the plural, Google produced quite a few results. That really puzzled me, so I decided to do some more searching and came across a Manisa Turkish page. The page, (which you can link to here: http://www.turkishlanguage.co.uk/defarts.htm) contained the following information:
... [bazı always governs a plural noun: bazı masalar = some tables]
That just states the rule, though. It doesn't tell you why. More than that, I later found a publication that says "bazı" can be used with a singular noun, supporting what I found through Google. The publication I found was Essays on Turkish Linguistics and in it was the following:
... when the quantifier bazı occurs with a plural marked noun, it is interpreted as "some"; with a singular noun, however, it is interpreted as 'a type of'.
So then I decided to take a look at a list of some indefinite quantifiers, applied them to English, and compared them to what I found in Turkish. From my observations, it appears that many indefinite quantifiers (e.g., a lot, some, little) can take both a singular and plural in both Turkish and English, but one is usually much more prevalent than the other and doing so alters the meaning to varying degrees. Most of the time, English favors a plural noun with these quantifiers and Turkish the singular. Some words, such as "many" and "few" are never used with a singular noun in English.
"Bazı" is the exception in Turkish. Why this is so, who knows, but I would guess that "some" is a word that is too ambiguous to automatically infer it is referring to a number more than one and therefore adding the plural suffix to the noun that follows it is not considered redundant.
Hope that was clear, helpful, and interesting in some way.
Note: After posting the above, I happened to stumble upon a web page that might be really helpful. You can link to it here:
Was this a "type what you hear" exercise? There, you're supposed to type what you hear, not the translation into English.
If you type something else (such as an English sentence), the error message may show you what you should have typed (in Turkish) together with the translation into English -- the latter for information only, not to imply that typing that as an answer for that exercise would be accepted.