We use mercury vapour exclusively with our beardies, and they do get hot.
With an enclosure that size, I'd go with a 100 Watt spot. We've use the original Active UVHeat bulbs, the T-Rex Active UVHeat & the ZooMed powersuns.
We haven't use Big Apple's bulbs, although we know somebody who has and we compared the UV output of both it and a Powersun with a pretty expensive UV meter (the meter cost about 400 bucks at Daytona last year).
Both bulbs we tested were 160 Watt Floods, and both bulbs were brand new (no more than a couple of days old), and they'd both been allowed an hour or so to fully heat up before testing.
Actually at the bulb the Big Apple bulb was putting off twice as much UVB as the powersun, but at 12" away from the bulb, the powersun was putting out twice as much UVB as the Big Apple. At 24" the Powersun was still more output than two 3ft flouresent UVBs (forgot the brand), but the Big Apple bulb was really low on the scale.
If I were you, I'd go with a T-Rex Active UVHeat or ZooMed Powersun 100 Watt spot. We use one of those in a 20g tank with two baby beardies in it. It gets the basking spot nice and warm without cooking the entire tank. The floods will radiate more heat throughout a tank as small as this, and you will probably find it does it with your tub too.
A 100 Watt spot will easily heat up a good 7-8" diameter circle at a distance of about 18" away, which is still throwing off plenty of UVB.
We use 160 Watt floods on the 65g tanks & custom enclosures for our adult beardies, and we also use one (primarily for its UVB output) in combination with a 500 Watt halogen (for the heat) in our outdoor Iguana Enclosures for those slightly cooler days. The outdoor enclosures are BIG (one's 10'x5'x7' and the other's 8'x3'x8') and neither of the iggies are showing any signs of MBD, or other problems. Of course, on the days when it's bright glorious sunshine (as happens quite often down here in FL) they're getting natural UVB from the sun.
One report I saw (url is below) put Texas at noon on an overcast day about halfway between the 100Watt & 160Watt Powersun floods (at a distance of 10"
as far as UVB output goes. So while even mercury vapour bulbs don't even come close to natural sunlight, they are the closest out there unless you want to go and spend several hundred bucks on a lighting system. 
The Importance of UV Lighting
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