The Sony D-NE300 for approximately $60 has been well received lately. I've got a higher end model, the D-NE500 and it's slick too. The menu system, features, and sound quality should be identical. I think that I would've been happy with the D-NE300 if I'd bought that.
The D-E350 is a 2-year-old model that doesn't compare to today's players in terms of the anti-skip. And the anti-skip (the older ESP Max, which relies solely on high audio compression in order to provide skip resistance) compresses the sound even more than any of the G-protection models. Its anti-skip can be turned completely off - but that would make the D-E350 virtually unusable for even walking around with while listening, as its skip- and bump-resistance with the anti-skip turned off is much worse than on most other PCDPs, even some of those much older players that don't have anti-skip at all.
Nor can that PCDP even remotely compare to the better 'vintage' PCDPs in terms of sound quality.
Furthermore, that PCDP used a headphone-out that actually rolls off the bass whenever any pair of headphones get plugged into that PCDP - and attempting to balance out the sound by boosting the bass will only result in badly distorted sound. And that's not to mention that its headphone-out is on the weak side to begin with.
In other words, that PCDP is just plain mediocre.
As for any PCDPs that provide "good bass", you're pretty much limited to buying an old (pre-Y2K) model used anyway. None of today's new PCDPs have enough power at their headphone jacks to provide the bass that you crave without having the output clip/distort badly.