How long did Gandalf fight the Balrog for?

[Legolas]

There's really no way to know, as indicated by Gandalf's account:

'Long time I fell,' he said at last, slowly, as if thinking back with difficulty. 'Long I fell, and he fell with me. [...] 'We fought far under the living earth, where time is not counted. Ever he clutched me, and ever I hewed him, till at last he fled into dark tunnels.'