The reason that you're not seeing a direct ride from Aberdeen to Inverness is because there is railway line work between Aberdeen and Dyce. ScotRail are laying on bus service, but I'm not sure if it is all the way from Union Station to Dyce. I suspect that it is.
You could resolve this by cycling out to Dyce, although I would imagine that ScotRail have considered that some travelers may have bikes. It's not that far out to Dyce. A96 to A947 is probably the fastest way. or you could follow the bus.
As far as your plan to follow the coast road up to Stonehaven, that is a very good road, gaining in attractiveness once you pass Montrose. If you're traveling in mid July, be careful around Carnoustie. The British Open is being held there this year, and there will be many visitors unfamiliar with driving on the left.
Arbroath is a very charming town. The Declaration of Arbroath was signed at the abbey in 1320. It was the basis for the American Declaration of Independence. The abbey is well worth a visit. You may also want to try some Arbroath smokies (smoked haddock).
There's not a whole lot to see in Montrose. It has a pleasant enough town centre, and a decent beach area. One thing you may want to look out for is a monument to Bamse the Sea Dog, a St. Bernard who was well known throughout the town during World War II. His story is very touching.
Between Arbroath and Montrose is Lunan Bay, with a hikeable beach.
Once you clear Montrose, the A92 follows the coast more closely. There are several charming fishing villages along the coast, well worth a side trip. St. Cyrus, Johnshaven, Gourdon, and Catterline are all very worth investigating. Lunch at the Creel Inn in Catterline would be a good stop, although they're a bit pricey.
Just before you get to Stonehaven, you'll see a signpost for Crawton. If you follow that dead end road down to the coast, you'll find Fowlsheugh Bird Preserve, which is probably the best place to see sea birds in great numbers along Scotland's east coast. There are thousands upon thousands of all kinds of gulls, kittiewakes, guillemots, razorbills, and the occasional puffin nesting on the cliffs overlooking the North Sea. The noise is amazing! Best place to see puffins is on the cliffs past the observation hut. Just north of the hut, go around the cliffs to your left, and look down from the north side of the cliff. There's a cave in the side of the cliff, where you're likely to find puffins.
Between Crawton and Stonehaven is Dunnottar Castle. You are probably already aware of it, and I'm sure that's why you included Stonehaven in your itinerary. Once you've visited the castle, you can take the high road in to Stonehaven, past the war memorial. There's a nice view of the town from there.
The A90 is about the only way to get from Stonehaven to Aberdeen. Be really careful while cycling. People drive that section of the road as though they were competing for post position at the Indy 500. If it gets to be too much, you can turn off at Portlethen, then follow the back roads through Findon, Cove Bay, and Nigg Bay. That way will take you in to Aberdeen at Girdleness, then it's an easy run past the dolphin watch and down to Torry.
While you're in Aberdeen, if you have time, Old Aberdeen is worth a visit, as is Duthie Park. The Winter Gardens at Duthie park have a wonderful botanic garden, which contains the largest display of cacti in Britain. Best of all, it's free! Old Aberdeen, especially around the university, would be ideal for cycling, as it's a rabbit's warren of one way streets. Watch out for the cobblestones, though!
I guess what I'm saying is go with option one!
Have a wonderful time!