What you want cannot be done out of the box with TFS.
However, I created an open source project called TFS Aggregator to give the support you are looking for.
You could setup an aggregation something like this:
<AggregatorItem operationType="String" linkType="Self" workItemType="Bug">
<Mappings>
<Mapping targetValue="Assigned" inclusive="Or">
<SourceValue>New</SourceValue>
</Mapping>
</Mappings>
<Conditions>
<Condition leftField="Assigned To" operator="NotEqualTo" rightValue=""/>
<Condition leftField="State" operator="NotEqualTo" rightValue="Removed"/>
<Condition leftField="State" operator="NotEqualTo" rightValue="Done"/>
<Condition leftField="State" operator="NotEqualTo" rightValue="Ready For Test"/>
<Condition leftField="State" operator="NotEqualTo" rightValue="In Progress"/>
</Conditions>
<TargetItem name="State"/>
<SourceItem name="State"/>
</AggregatorItem>
That should move your bug to Assigned from New.