Aberdeen -walking to Dunnottar Castle

I've stayed at the Ibis. It is an excellent location on the Shiprow opposite the Maritime Museum, in walking distance of everything.

I believe the Tourist Information Centre closed last year, but if you look at the Visit Scotland website you should be able to find something. I actually have a paper street map of the City on my desk at the moment, and would expect you would find one in a bookstore in the Union Square Mall (adjacent to the Bus and Rail stations).
To Dunottar the X7 bus (to Dundee) runs hourly from Aberdeen Union Square via Stonehaven and stops at the road end,at a bus shelter with a grass roof.
I recommend getting the bus there, then walking back into Stonehaven.
Do check before setting out, as the Castle closes in windy weather.
There is also an hourly bus #8 back from Stonehaven to Aberdeen, so two buses an hour.

I spent a day in Aberdeen last month and historical Union Street, the main shopping street in the center, was torn up for construction. Quite a mess.

From the Dunotter Junction bus stop to the castle it’s supposedly a 16 minutes walk depending on how fast you walk. The first part is level, then you go down about 200 steps and then more back up to the castle. From Stonehaven itself, the walk is about 45 minutes parallel to the shoreline. Both times I’ve been to the castle I had a rental car. It can get very windy and could be cool, so have adequate clothing.

The Walk Highlands website has details and a map of the walk between Stonehaven and Dunnottar castle.

The Dunnottar Castle website has information about getting to the castle from Stonehaven. As well as the X7 bus mentioined by isn31c, there is also the 107 bus. (You can check and plan your journey using this website.)
Ask the bus driver to drop you off at Dunnottar castle junction.

something to bear in mind is weather and particularly wind..... The castle can be shut at short notice close with by very strong winds.

It may be a 16 minute walk (suspiciously exact) from bus stop to Castle, but it is only 5 minutes to the car park, toilets and pretty good cafe. That is to say that it is 10 minutes walk even from the car park.

If you are up for a largely flat hike then do consider the wonderful cliff top path from Stonehaven Harbour to the castle.On a decent weather day, it's a glorious walk, busy yes but the finest way to approach the site.

Sorry, it's not entirely flat...there is a considerable set of steep steps from the harbour to path start! A bit of huff and puff to get up them! Forgot about that bit.A little gradual ascent to the cliff top , a minor downhill section then flat( from memory!)

Is there a specific reason why I wouldn’t take the train from Aberdeen to Stonehaven and then walk to the castle?

Is it because talking the bus from Aberdeen to the bus stop above the castle will reduce my walking time (so I wouldn’t have to walk 2km there and 2 back)?

Would it be possible to take the X7 bus there, see the castle, walk on to Stonehaven and then take the train to Aberdeen?

I think the castle website is suggesting walking from Stonehaven to the castle and back again.

There is no reason at all not to walk both ways, or to take the train one or both ways.

Train one way and bus the other will be more expensive, but apart from that it's fine. Personally I always favour a round trip, as opposed to retracing my steps but that is personal preference.

Walking FROM Stonehaven builds the suspense as the Castle comes into view, and the faux greek temple which is Stonehaven war memorial adds to that.

As long as you know all the options, how you juggle those options and the attendant cost is up to you.

It will be easier to walk back from the castle to Stonehaven as you will be going down the steep steps from the town.But as said, it’s also lovely to have the castle get ever nearer as you approach it along the cliff path.
Weather and wind direction might come into play on the day!