17A from Howth Junction would get you close enough, also 104 from Kilester
17A probably best as its one less change though it would be a longer walk from the Bus to Artane shopping centre. Say 5-10 minutes walk at each end, 15-20 minutes on the bus from Howth Junction
Sadly you can't get a bus/rail ticket from Drogheda to cover this
Advisable to get a Drogheda Dublin rail ticket so you have multiple options on the bus, eg 27b from City Centre
Howth Junction isn't a nice place to be after dark
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