I've followed TB for some period of time, and based on the many knowledgeable people here, I've compiled a list of factors that will affect your P-Bass tone. I recommend working through these one by one, with straightforward A/B tests to dial in the tone you want.
Variables that affect how my bass sounds, according to expert TB posters:
Bass:
1. Pickup brand, model, design
2. Pickup height
3. Pickup angle
4. Pickup position
5. Pickup magnet material
6. Number of pickups
7. Blend of multiple pickups
8. Scale length
9. Bridge design (high mass, low mass, etc.)
10. Body wood (single piece, multi, laminated)
11. Body shape
12. Body design (solid vs. semi-hollow vs. hollow vs. archtop)
13. Body finish (nitrocellulose, Danish Oil, Poly, earwax)
14. Neck-thru vs. bolt-on vs. single piece
15. Nut material (bone, brass, Corian, etc.)
16. Neck wood (single wood, multi-part)
17. Fingerboard/fretboard wood
18. Fingerboard/fretboard finish
19. Neck thickness
20. Headstock design, mass
21. Passive vs. active electronics
22. Preamp brand
23. Components: pot characteristics, cap values, etc.
24. EQ design: 1 band, 2 band, 3 band; cut vs. boost, etc.
25. Tone control settings
Strings:
26. String brand, model, endorsing artist
27. String design: flats vs. rounds vs. half-rounds
28. String materials (nickel, SS, TI, metallurgical charasteristics)
29. String coating
30. String gauge
31. String core material, core shape
32. String age
33. String tension
Instrument Cable:
34. Brand
35. Wire gauge
36. Cord length
37. Connectors (gold plated, chrome, nickel, brand)
Amp:
38. Tube vs. solid state
39. Amp design (A, AB, D, etc.)
40. Tube preamp vs. solid-state preamp
41. Amp brand
42. Amp power rating
43. Impedance characteristics
44. Separate amp and preamp or integrated
45. Country of manufacture
46. EQ settings
47. Tube manufacturer
48. Component quality
Speaker Cable:
49. Cable Brand
50. wire gauge
51. % purity of copper
52. Cable length
53. Connectors (Speakon, ¼ phone, banana plugs, automotive jumper cables)
Speaker Cabinet:
54. Separate cab, or combo
55. Size of driver(s)
56. Number of drivers
57. Manufacturer of driver(s)
58. Driver design (magnet material, cone material, impedance, etc.)
59. Age of drivers
60. Ported or sealed
61. Port design and placement
62. Cabinet dimensions
63. Cabinet materials (ply vs. MDF, vs. birch vs. tissue paper)
64. Cabinet coverings or finish (carpet, Tolex, stained and poly, etc.)
65. Cabinet position (distance from floor, walls, etc.)
66. Tweeter (design, placement, crossover characteristics, etc.)
67. Number of cabinets
68. Relative position of cabinets to each other
69. Relative position of cabinets to player
70. Relative position of cabinets to audience
71. DI vs. micd cabinet vs. no sound reinforcement
72. Use of FOH system (plus skill of operator, etc.)
Room acoustics (includes about 1 trazillion variables here)
Psychoacoustics:
73. What the bassist paid for his/her bass
74. What the bassist paid for his/her amp
75. What the bassist paid for the cabinet(s)
76. What the bassist thinks about his/her equipment
77. What the bassist thinks about his/her own skills
78. How rested (or hung over, or intoxicated) the bassist is
79. What the bassists experiences were with other equipment
80. What the bassist remembers about other equipment
81. What the bassists hero uses
82. What the bassist remembers about his/her heros playing
83. The bassists individual neurological characteristics (hearing acoustics, tinnitus, sense of pitch and timbre, etc. etc. etc.)
84. What the bassists girlfriend (boyfriend) thinks of my sound
85. What the bassists guitarist (drummer, horn section) thinks of the sound
86. What the bassists BBF thinks of the sound
87. What the soundman thinks of the sound
Playing technique:
88. Touch (digging in or tickling the strings)
89. Angle of pluck
90. Pick, fingerstyle, slap, etc.
91. Position of hand in relation to pickup(s), bridge, neck
92. Angle of fingers in relation to strings
93. And, of course, the players mojo, groove, and funk-icity