Yes, and there's several approaches to it!
You can use the field context to say "this field only applies to bugs"
You can use field configurations (you have one with the field shown, and another with it not shown, and use a "field configuration scheme" to say the 1st one applies to tasks, and the second for bugs)
You can use screens to do it - tell jira that a set of screens including the field should be used for tasks, and a second set without the fiel for bugs
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