How can I achieve this sound...?

[ultimabass]

To gliss down on your fretboard, but without the additional "fret transition" noise. As if on a fretless bass!

[king_xanadu]

im no expert, but...
my guess is really fast
or a fretless

[René_Julien]

maybe the "defretter" effect like in the BOSS multi's?
don't know, never tried it myself.

*cough* get a fretless.

no pain no gain, no frets no worries.

[niftydog]

A Whammy, a whammy or a fretless.

[Thunderthumbs73]

Get a fretless.
Turn the treble all the way down on your bass so those noises are minimized.
Slide quickly so that the those noises will have minimal chances to be heard.
Other than that, get a fretless.