If you have a fixed number of Name/Value pairs you can do this
SELECT TOP 1000
[AppActionNameID]
,CAST([AppActionParams] AS XML)
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Name[1])[1]','varchar(20)') AS Name1
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Value[1])[1]','varchar(50)') AS Value1
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Name[2])[1]','varchar(20)') AS Name2
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Value[2])[1]','varchar(50)') AS Value2
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Name[3])[1]','varchar(20)') AS Name3
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Value[3])[1]','varchar(50)') AS Value3
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Name[4])[1]','varchar(20)') AS Name4
,CAST([AppActionParams] AS XML).value('(/BounceProperties/Value[4])[1]','varchar(50)') AS Value4
FROM [myschema].[mytable]
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Deja View - The strange feeling that somewhere, sometime you've optimised this query before
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http://www.sqlservercentral.com/articles/Best+Practices/61537