Is there software available to burn audio/mp3 files to a DVD disc without gaps?

Your best bet might be to edit the audio in a program like garage band or Anvil.
Bring all the pieces into it, cut the gaps as you like, publish the result onto optical disk.

I have used CDBurnerXP for this purpose before. link

Despite the name, it does DVDs as well. My recollection is that it relies on the input file(s) for spacing and pausing.

If you are making a CD that plays on CD player (ie a normal audio CD) then the maximum length is 80 minutes. You can use your burning software to control the gaps between tracks including leaving no gap so it plays as on continuous piece but you can’t have more than 80 minutes.
If you’re recording MP3 as data that can only be played on computer or device that knows what an MP3 is then you can probably fit 3–4 hours at a reasonable bit rate.