The first Bass Strait crossing by a jet ski was done from the Great Australian Bight to the Tasman Sea by the Oztrek2000 team during their cicumnavigation of the mainland in 2000.

Tony Ringrose on a Yamaha SUV departed Port Welshpool on 2nd of May 2003, stayed with friends at Flinders Island and ducked over to Tas mainland just to finish the trek. Tony towed fuel in a rubber dingy behind the vessel and carried a pillion.
He reports using 300litres of fuel on the way over as the weather turned nasty and much of the trip was a hard slog.
Tony's SUV broke a driveshaft on the return journey (8th May)about 20k the Flinders side of the Kent Group.
Tony was able to call on his ample support group from among the Flinders Island community who came out and towed the craft back to Whitemark with a Shark Cat.
It was noted that Telstra CDMA digital services were used to communicate from the disabled craft to Flinders Island. Much of this route is now covered by Telstra CDMA and it is advised that if a satellite phone (recomended) cannot be obtained, a minimum of at least a Telstra CDMA handset be carried as well as the usual safety communications gear. (HF/VHF radio, Epirbs etc)
Tony's comments : "I don't recomend it, but if you must do it - take plenty of fuel!"

The second crossing was done by a pair of local boys from Port Welshpool, Mark Bland and Peter Boyd. These daring lads did the trek to Bridport via Flinders on modified stand up ski's. The lads departed Port Welshpool on the 7th of May 2003 and arrived in Bridport the next day.
The Yamaha 700 Superjets had an addition 100 litres of fuel carried in 20 litre jerry cans. These cans were strapped into aluminium frames that ran along both sides of the vessel, with an additional Jerry can placed on top. The fuel was attached to standard Yamaha fittings and connected to the reserve fuel system. Each container was then connected in turn and utilised by the machine.
Mark reported having some difficulty getting fuel from the rear drums at times, and some drum shuffling was done.
The machines were refueled at Whitemark.
Mark and Peter camped on Cape Barron Island overnight as they were running out of daylight and Banks Strait was standing a bit to high for comfort.
They proceeded the next day to Bridport.
With no sign of good weather for the return trip, the boys flew back and the craft are being shipped back by surface.
Mark's comments : "I don't recomend it!"

The first solo (unsuported) trip was done by Ron Ipsen (aka scuzzi) on a the modified sea doo gtx s/c described on this site. Leaving Port welshpool on the morning of may 27th 2003. Ron pulled in to Killiecrankie bay that evening to refuel after stopping at Bulli bay (kent group) for a coffee break.
Killiecrankie Enterprises put Ron up for the night and in the morning he continued along the west side of Flinders Island heading down to Musselroe Bay to meet media at 3 pm.
The weather turned as he came into the Tassie mainland and the return trip was called off for safety.
Ron's comments : "I don't recomend it! but if your gunna try, be very careful!"