Hi
Not a total expert on these older seadoo's only really had a 951 di model but.....
It's quite common to see folk fitting priming bulbs on the line between tank and carbs. My yam GP800r has it and helps massively when starting, because I always run it out of fuel after each use by shutting the fuel valve when retrieving at the ramp.
That said...if you are getting air in the fuel lines, it might suggest that you are drawing air through an open to atmosphere leak....like the fuel filter inlet and outlet not being tight enough. Have a look and make sure the pipes are all tight.
Either that or your fuel pump, feed to carbs or carbs are/ is drawing air.