BB's never displayed enough FIRE power to set a city on fire. And blasts of fire is nothing Spider-man cant dodge with his eyes closed. Johnny Storm is a good example. Plus web-shield were shown to be resistant to fire even from a magically amped dragon. Also dragon is a big target. BB will get his eyes ripped out with SpOck's claws if he stays in that form. His safest bet is to mix shapes. His most common animal forms just wont cut it. Not to mention all combatants fight in character. Its not like Garfield to set people on fire. While Spock wont think twice about killing BB.
Actually it would be quite difficult for BB to beat Spider-man. Any animal that get's close to spidey's strength class is far too slow to keep up with him, anything fast enough really isn't a threat, plus spock(and peter) have tech and the Spider sense. I'd give Pete or Spock the majority in character.