Traveling from Dubai to Abu Dhabi when arriving from Houston IAH – assuming that Abu Dhabi is your final destination upon flying in – is a bit cumbersome. Once the flight lands at 7.35p, you wait for about 20-30 minutes for the baggage at the Dubai DXB airport and head over to Customs. If you look remotely Indian and have a cart full of baggage and try to go through the Green channel – nothing to declare – nice try. The security officer will direct you towards the scanner for contraband or items that you ought to declare.
Standards questions – how long are you staying, the purpose of the trip, where are you headed and, the proverbial, do you have any medicine? In childhood, someone may have shared with you the wisdom that “honesty is the best policy” and this would be the ideal time to practice it. I mean think about it, the scanner shows the contents of your bags with some things color-coded that stick out like a sore thumb. If you do have meds, be sure to have the prescription to back it up. Best to have the meds in the original pharmacy bottle with the label in your name on it. Just saying…
So, by the time you exit the Customs area, say it is 8.30p or so. Head upstairs to the food court – as of this writing on February 8, 2020, the downstairs food court is undergoing repairs or renovations. Grab a bite to eat, take your time. The Emirates courtesy or complimentary bus to Abu Dhabi doesn’t leave till 11p. Now, here is the catch, you must or should have booked the ticket to Abu Dhabi from Houston to include the bus service. No extra charge but, I wouldn’t take a chance of hoping to hop on the bus once you land in Abu Dhabi. There are only five-time slots for when the bus leaves from Dubai. And, an interesting twist to this Emirates Air complimentary bus service is that it is only for folks traveling on economy class. Huh? For a change, I feel privileged 
Now, here comes the less than desirable part. GOOD LUCK on figuring out how to find the bus. Zero signage, zero instructions. Follow the sign at the Dubai arrival terminal for buses, metro, public transportation, etc., on the SECOND floor. Go through the car park building. Upon exiting the building, turn left and keep walking till the road curves to your left and you will see a bus parked there. You won’t see the bus as soon as you turn left upon exiting the car park complex. If it weren’t for the gentlemen manging the pedestrian crossing helping me out by telling me how to get there, it would have been a long walkabout with my luggage cart. Once you get to the bus, don’t expect any action till about 20 minutes prior to departure when the bus driver will arrive and load the luggage in the belly of the bus. Then, another gentleman will arrive and ask for your boarding pass (hopefully, you didn’t toss it after clearing Customs!) to verify that you are booked to travel to Abu Dhabi.
It takes a good two hours, perhaps a bit over to get you to downtown Abu Dhabi. Plenty of taxis available at 1a to take you to your destination. The bus ride is comfortable and chances are you are going to doze off. Emirates could surely do a better job at a minimum of two things:
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Enquire and inform the Customers traveling to Dubai if they are planning on going to Abu Dhabi
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BETTER SIGNAGE or instructions on how to find the bus!
BTW, there is no private shuttle service between the two cities from the airport similar to shuttle minivans found in the US where for a reasonable price you share a ride with others. Nor is there a train service between the two cities. Word is that the train service is a work in progress as part of the nationwide UAE railway network. That would be cool!
Note that you can also take a bus from Dubai airport to downtown Dubai to Abu Dhabi. Of course, the hassle here is that if you have two full-sized checked-in suitcases and carry-on luggage, you are going to have to haul it around.
MORE INFORMATION
https://dubaiofw.com/dubai-to-abu-dhabi-bus/
https://www.rome2rio.com/s/Downtown-Dubai/Abu-Dhabi