Tico Tico no Fuba is a Choro (translates as Crying or Weeping in english).
This kind of music is related to french influences on afro-brazilian forms somehow like your traditional Jazz from New Orleans (including all the interplay and improvisation) and is the beggining of brazilian's modern muscial forms alongside the more well known Samba.
In the CD Box Verve Years, from Charlie Parker, you can hear him playing that Tune. Carmen Miranda recorded it too, but it sound better when heard by the traditional instrumental from Choro's combos because everyone is kind of soloing at same time.