I don't think that there was an other way around or over the chasm. What proteting would the bridge have been if there was an other way?
But the Orcs were seen greatte numbers at the border of Lorien the same night as Gollum. We can assume that they bridge the chasm sone after the fellowship left Moria. Probably the Orcs waited for the night, before they came out of Moria but Gollum could have moved earlier.
Respectfully
Findegil
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