I would suspect the answer is that it is legal in your case, although it will vary from font to font, and what follows is advice to help you find out more and decide for yourself.
Font/typeface files are copyrighted, but the actual typeface itself may not be, at least in some jurisdictions, including the USA it seems. But if you want to sell internationally, it's probably wise to assume the font is under copyright.
If we assume this is true, then by default nobody but the owner has the right to distribute copies of the file or any other work derived from that file or the creative work within (ie. the shape of the font), including bitmap images. However, typeface designers know that this would cripple the usefulness of the font, and thus they usually distribute the font to app and OS developers under a license that allows them and their users to use that font in the creation of their own documents. Some licences even explicitly allow the font to be embedded in a document (eg. as commonly done in a PDF). However, the licence usually prohibits you from distributing the font itself, because they wish to reserve that right (so that they can sell it, obviously). And some designers are not so lenient with their licensing - one company quotes $900 for an iOS app use, for example.
So the question becomes more nuanced - is your bitmapped version of the font considered a document created with the font, which is usually explicitly permitted for distribution? Or is it considered a transformed copy of the font, where redistribution is explicitly denied? Obviously it is both, but the following factors may help decide how it will primarily be viewed:
- Are you redistributing the font to someone who wouldn't legally be able to use it anyway? In the case of a system font you are not, so this is fairly uncontroversial - both parties have the right to use the font in their own documents so it would be hard to argue that you need to buy an extra license for this purpose.
- Are you embedding the font in the app? If you put the bitmap into the binary, or otherwise obscured, rather than leaving it as a standalone file that is easily extracted and reused, then this will typically fulfil the embedding requirement and make it an authorised usage (if indeed the licence for the font permits this).
- Are you distributing it in a form that replaces the need for someone else to license it legally? If your app allows easy extraction of the font, or lets people arrange the letters to produce text in that typeface for their own documents (eg. you're selling a mini Photoshop clone), then that is very likely to contradict the spirit of the licence even if the wording is not clear.
Ultimately though, as with most legal questions, it comes down to a question of probabilities - you can't guarantee you won't get sued even if you follow the law to the letter, only that you'll win if you can cover the legal fees long enough to see the case through. Similarly you can break a licence and you may get away with it - and in this case, the licence may not even be meaningful due to the USA court ruling that fonts themselves cannot be copyrighted. But it's a gamble.
The safest thing to do is to select a font that you are explicitly allowed to use in this way. In addition to the links that Mr Beast provided, I like to recommend FontSquirrel as the quality of fonts there is very good and the licences are generally very liberal.