Sidewinder suicide means:
1) buy a stock sidewinder/hauler/whatever you can get cheap, and fly it, leaving your good ship safely docked.
2) get it blown up (I think sitting in a star's corona is more satisfying than self destruct)
3) choose not to rebuy. You will respawn with a free sidewinder at the first place you docked after leaving the starter zone, which, unless you were a super-stud and went from Dromi to Colonia without docking or landing, is in the bubble somewhere. Your main ship will still be where you docked it at Colonia, as will your carrier, etc.
Personally, I would just fly back in my explorer, get what I need in the bubble, and return to Colonia in my explorer. (Actually, I would probably rage quit, or play something else until the problem gets fixed, like I did when there was a Thargoid invasion instead of a rebalance to engineering). Given the number of bugs that never get fixed, though... this one worries me.