Sure, ガム can be used to refer to bubble gum. 

ガム is short for チューインガム, and according to 広辞苑, 風船ガム is a type of チューインガム:

> <strong>ふうせん-ガム【風船ガム】</strong>  
> 　息を吹き入れて風船のようにふくらますことのできる<strong>チューインガム</strong>。

And if you look online, you can find people saying ガムを膨{ふく}らます.  Sure, sometimes they write 風船ガム, but sometimes it's just ガム.  For example, take a look at [this question on OKWave](http://okwave.jp/qa/q2696097.html):

> <strong>ガムを膨らます</strong>ことが出来ますか？  
>
> ...
>
> そこで質問なんですが、あなたは<strong>ガムを膨らます</strong>ことが出来ますか？  
私の回答は「<strong>風船ガム</strong>ならいつでも可、<strong>普通のガム</strong>なら二個以上なら可」です。

Here, they talk about how they can always manage to blow bubbles with 風船ガム "bubble gum", which they compare to 普通のガム "regular gum".  And the question title simply says ガム, which appears to be a hypernym of both 風船ガム and 普通のガム.  If ガム really didn't include 風船ガム, the question title would be confusing, and they wouldn't have had to specify 「普通の」 in the question body&mdash;just saying ガム would be enough.  Obviously, that isn't the case! 

The same goes for the top answer on the question. Here's an excerpt:

> <strong>ガムを膨らます</strong>ことは出来ました。  
> <strong>どんなガムでも</strong>OKです。

You can find plenty more examples like these.  As you can see, people don't have trouble understanding 風船ガム (or バブルガム) as a type of ガム.