Second order harmonic distortion?
 

How can I achieve this without a tube amp. Any recommended gear?

Anything less expensive?

Aren't there 100 overdrive/distortion pedals out there that do this?

That would be my question too.

Can you say more about the sound you're trying to achieve? Distortion pedals can be very different in character...

Without further input, I'd say you might want to look into the Tech 21 VT Bass pedal, especially for nailing those retro tube amp sounds. For even bigger distortion, the Darkglass B3K is getting a lot of attention. If you want something with a DI attached so you can send an ampy sound to the FOH, look into the SansAmp Bass Driver DI, the Hartke Bass Attack, The MXR M80 Bass DI+, the Aguilar Tone Hammer and the Darkglass B7K.

But all these units are really different from one another. Everything depends on the kind of distortion you're looking for.

Thanks for the suggestions. I have the fist model of the Sansamp VT Bass pedal but unfortunately it doesn't have speaker simulation defeat switch of newer models.

IIRC, adding second order harmonic distortion is not like OD or distortion from a pedal, but adding more of a "fullness" to your tone, something very pleasing about it when it is there. Your best bet is to try and find a used MusicElectronix/Zeibek Submarine. They show up used around here on occasion. Mine isn't going anywhere.