I'm late coming to this discussion so it's possible no one is paying attention anymore. You do need a smart phone for these apps but the apps are free.
The two I have used are Google Transcribe and Otter Voice.
I bought a cheap ($50) Android for Google Transcribe. Like Shari Eberts, I wrote enthusiastically about it on my blog. I was thrilled to have any kind of speech to text app after all these years. I chose not to get phone service on the Android, however, since I already have an iPhone and phone service would have greatly added to the expense. That meant I had to have wifi to get Google Transcribe, and often it wasn't available.
Now I have Otter Voice on my iPhone and I'm impressed. You need cell or wifi. Smart Phones work fine on wifi. You can even make and receive calls by going into settings and allowing wifi calling. Unlike Transcribe, Otter Voice puts a line break between each speaker, it can identify them if you give a name (otherwise it's "Speaker 1", Speaker 2, etc.) and it even punctuates. I used it in a complicated meeting of four people recently where a lot of technical terms were used. I was amazed at how accurate the transcription was.
On the subject of live captions, Innocaption has also been life-changing for me. I have had a desk captioned phone for years, but I have never been able to use my smart phone for calls. Now, thanks to Innocaption, I can make calls anywhere and have live captions.
Innocaption and Otter Voice are free. You can pay to upgrade if you use them a lot and want additional features