You only have to listen to some records do realise that Analog Synths is the proven and original Synthesizer.
Monophonic is always the choice for good bass lines , you need sub frequencies and a method for creating overtones (oscillator tuning, VCA control and a way of routing these differently) the overtones can then be swept of cutoff by a VCF (filter) the filter is the foremost important part of a synthesizer and will make the room shake when Resonated

For your budget you may think you will never get to the MOOG, OBERHEIM, SC, ARP level but there are a couple of Magical instruments that give this actual circuitry without all the expense of hand built wiring looms and expensive potentiometers (Pots/knobs/sliders/ribbons/matrixes)
My personal favourite is the Oberheim Matrix 1000 .. this is entirely Analog in its Signal path and does have 6 voices ... which pack a punch if used in UNISON (all voices consisting of 2osc per voice , thats 12 oscillators in total to make one key if played in mono ... The Matrix1000 has legendary Presets giving a good start point for the type of sound you want .. and 200 user presets for storing your own Patches ... I'm assuming you have already googled a picture of this and are thinking "what it looks like a digital rack synth with no knobs!!" well it does look like that , but now google the Oberheim Matrix 12 or Oberheim Matrix Expander ... yes these do cost £2000 puls these days and not with out good reason !!! They have been used by most of the recordings from the late 70's ,80's 90's and their predecessors the OBXa etc have been used since late 60's early 70's
So if I told you that the |Matrix 1000 has the same exact sound board as the £2000 Oberheim Matrix would you believe me

well the matrix 12 has 2 of these boards but the Expander has One like the Matrix 1000 ... but if you were to get more than one say 6 you would have a stupidly powerful Analog Studio (Aphex Twin uses them for his source sound ) but to get 6 Expanders well that would be near on £20,000 so to get your foot in the door by one Matrix 1000 with a view to getting another for the ability to play more than one sound at a time !!!
Even though I'm talking about using it as Monophonic with all voices in Unison .. it is of course a full 6 voice polyphonic Synth and most famed for its mid range pads .. but I am just highlighting the mono unison features to get a powerful method for bass !! Analog!! and heres the best part .. Full Modulation and patch creation facility via computer hookup , yeah you can see the entire guts of the sound board right on the computer screen.
google "Midiquest Matrix 1000" or "SynLibMx6" to see the editor librarians for PC there are Mac ones too but I'm using PC ..it was orinally shipped with an editor for Mac O.S.7 i think.. and was designed to be a cost effective method to get the analog boards out there to the market during a time that japanese, taiwanese factories were wising up to cheap labour and build costs of US companies .. hence the start of many Japanese digital synths flooding the market.
the latter is really designed for the OBERHEIM MATRIX 6 which again is the same sound board and processor as the 1000 but is stereo output and allows for 2 split sounds to be played at a time in mono (one output) each these cost around 400-600 and are worth the stretch , but give me 2 x 1000 any day for the same price and one dedicated to bass the other to pads!!!
So the Matrix 1000 for 250-300 bucks is a must ... the only let down is that more than 4 realtime controllers can flood the processor , which is a smaller processor than the Matrix 12 / Expander that is the main difference on the design of the oberheims !!! the amount of realtime MIDI modulation !!
Don't pay attention to some forums websites that say you only have one realtime Modulator as I have 4 programmed on mine plus pitchbend and aftertouch so thats 6 in all ... which is just enough for me on one sound , given the Matrix is named so because it also has an internal matrix to make various sources (Velocity,LFO1/2,VCA,ENV1/2/3, etcc) control many destinations (VCF,LFO,VCA,OCS1/2/mix,RES,FM..etc.)
the possibilities are endless and the sound so pure you can "physically smell/hear/sense" the clarity and nuances .
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Other synth worth checking especially if you need that Moog filter or SEM or Arp Filter sound is the Analog Tone Chameleon ATC-1
They go for about 400-500 but have the actual Analog filters built on optional cards and ships default with the MiniMoog famed Ladder Low pass filter ... again the synth looks like a digital rack synth but is completely Analog in its sound signal path ( when i say this I mean "only the parameters are controlled via digital" the sound signal is pure analog though) saving you all that cash !! to get the chance to chain up more than one to make a motherlode Analog studio .
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There are other good analog synths , albeit new ones like the Arturia Minibrute advertised everywhere ..excellent for hands on creativity but not my favourite for bass (clean bass) good for dirty sounds etc..
The Novation bassStation has a new model mk2 , hav'nt tried this but I own the mark one which is amazing and was used on a lot of recordings in the 90's De La Soul "Stakes is High" LP yo name one ... This appears in rack form and keyboard form ..I believe the rack is 4 part mulit (don't quote me though) but yeah the bassStaion does exactly what it says in Analo too !
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There are many to chose from so best to rersearch the recordings you love to see what they were using and if its an analog synth its probably an Oberheim or Moog ...hence my reason to mentin an get the MATRIX1000 or The ATC-1
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theres a lot of funk records that sound like synth bass but actually are bass guitar processors / pedals / synth pedals / or in some amzingly creative cases bass guitar through moog vocoder/ moog filter / or analog filters ... the ATC does allow inputting through the filter whilst having envelope followers contolled with midi etc...
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I personally am getting the NEW Moog Sub Phatty soon ... which offers all the above and the ability to get inside the parameters via a computer ...very exciting thing indeed ..fatter than the other moog phattys due to the addition of a sub oscillator but these are 800 bucks in UK money so thats what 1100 in US.. but worth getting in time but are just monophonic yeah!! so I will still be using the Matrix for pads and midrange ...
wow I can go on when people ask good questions ...
hope that helps ,
back to playing now ,
" its Saturday a Saturdaaaayeeyaay "
JZA