The Anaheim Resort Transit (ART) shuttle doesn't go to Buena Park. Many area hotels have their own shuttles, but I don't believe the Fairfield in BP does (call and check with them). If there's no hotel-supplied shuttle, your options from there would be the city bus (OCTA), a taxi each way, a private shuttle or town car each way, or your own vehicle.
The Fairfield is pretty far away from the DLR. I mapped it on the OCTA site and it looks like the trip would take 51 minutes and one bus transfer. Unfortunately there's no bus that goes directly from your hotel to DLR

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As far as taxis go, your hotel is located in the triangle between the 5 freeway and the 91, west of the 91/5 split. The most direct route to the DLR would be the 91 freeway to the 5 freeway to DLR, or surface street to the 5 freeway to DLR. The taxi will most likely take one or both freeways.
A private shuttle could get pricey, and if you're concerned about time, then know that shuttles will give you a ballpark range for when they will arrive, which they usually do but you could get stuck standing there for a few minutes.
If this were me, I would take my own vehicle and park in the Toy Story Lot. Mickey and Friends can get backed up at the trams and sometimes you have to wait one or two trams before there's room. I generally count on 30 minutes from entering M&F to entering the park, slightly longer if there's a lot of people and few trams. My average time from parking lot entrance to park entrance from the Toy Story lot is about 10-15 minutes. So that's what I would do.
Hope that helps!!