I've taken the F55 bus to Dubai World Central Airport (DWC) a number of times when living in the UAE. This airport is also known as the Al Maktoum International Airport. A picture of the bus stop at the DWC airport is the tall sign on the left of the picture below.
The fare was 4.10 dhs and the bus goes from the IBN Battuta metro station to the new DWC airport (or vice versa) with almost no stops inbetween. This F55 bus trip took about 40 minutes and that was in fairly heavy traffic on a Thursday afternoon. The bus is limited how fast it can go on the motorway, so that time-frame will probably be fairly constant in the 30-45 minute range. Leave yourself plenty of time to catch your flight! There are now 10 stops on this route, going to a few stops at different offices and cargo terminals at this airport and they have even added a stop at Jebel Ali Gardens neighborhood, which is where I used to park my car (at a friend's place) when flying out of DWC
You will need a Nol card as Dubai buses no longer accept cash payment onboard. This can be obtained at the metro station, but for those flying in, you will have to ask where to buy them from. The Silver Nol Card costs 20 dhs, with 14 dhs credit included, and is valid for 5 years. You can recharge or add credit at machines at all metro stations and some other areas such as the large Ghubaiba Bus Station near Diera.
On returning to DWC, I got a taxi to IBN Battuta, which took about 20 minutes and costed me 60 dhs. Since there is only 1 bus per hour you might be better off taking a taxi to the Jebel Ali metro station. That's the first station on the Red metro line, which goes all the way across the city past the other airport. If I did that, it would have probably cost around 40 dhs instead. The fare into Dubai's city centre could be 200 dhs or more depending on traffic so transferring to the metro is a great way to save money. Once at the metro station, you could then buy a Nol card and get basically anywhere in the city for less than 10dhs; be aware the metro service stops around midnight if you are arriving on a late flight. Schedules could have changed due to Covid so check the RTA's Public Transportation's Website for more info!
According to RTA, the F55 bus is running ONCE EVERY HOUR 7 days a week during the times below (as of February 2022). Notice the time change on Fridays, which is the day everyone usually has off, so expect full public transportation across the city!
