How long does it take to get by taxi from Dubai to Sharjah airports?
It really depends what time you leave day on weekend or week day. As LP members said give your self enough time.
I would say, it can take up to 1 hour to 45 mins.
Edited by dan30

A taxi costs around AED100, or a little bit more if you are taking it from Dubai airport given the airport charge.
I dont think there is a direct bus, but I think the Sharjah transport people run a bus from Sharjah Airport to the closest Dubai Metro station, so you'd have to take a metro from the airport to Rashidiyah, and then a bus from there.
Try a search for Sharjah public transport to see if you can get a timetable.
Hmm - I cant find anything about that bus other than the fanfare PR stuff when it launched a year ago.
I dont think it exists anymore.

Are you by any chance flying with Air Arabia from Sharjah Airport? If so, they have a bus from Dubai to Sharjah Airport which takes an hour:
http://www.airarabia.com/sharjah-airport-dubai-bus-service
Otherwise, getting a public bus from Dubai to Sharjah and then onto Sharjah airport is probably possible, but likely to be a complete pain. A compromise option would be to take the Dubai metro to either Rashidiya or Al Qusais (opening shortly) and a taxi from there. Those are the closest Dubai metro locations to Sharjah Airport.