What we can infer about Bellatrix from her wand
Source: Pottermore
Her wand: 12¾" long, dragon heartstring core, Walnut wood, and unyielding flexibility
Wand Core: Dragon Heartstring
As a rule, dragon heartstrings produce wands with the most power, and which are capable of the most flamboyant spells. Dragon wands tend to learn more quickly than other types. While they can change allegiance if won from their original master, they always bond strongly with the current owner.
The dragon wand tends to be easiest to turn to the Dark Arts, though it will not incline that way of its own accord. It is also the most prone of the three cores to accidents, being somewhat temperamental.
Wand Wood: Walnut
Highly intelligent witches and wizards ought to be offered a walnut wand for trial first, because in nine cases out of ten, the two will find in each other their ideal mate. Walnut wands are often found in the hands of magical innovators and inventors; this is a handsome wood possessed of unusual versatility and adaptability. A note of caution, however: while some woods are difficult to dominate, and may resist the performance of spells that are foreign to their natures, the walnut wand will, once subjugated, perform any task its owner desires, provided that the user is of sufficient brilliance. This makes for a truly lethal weapon in the hands of a witch or wizard of no conscience, for the wand and the wizard may feed from each other in a particularly unhealthy manner.
Wand Length: 12¾"
Longer wands might suit taller witches and wizards, but they tend to be drawn to bigger personalities, and those of a more spacious and dramatic style of magic.
Wand Flexibility: Unyielding
Wand flexibility or rigidity denotes the degree of adaptability and willingness to change possessed by the wand-and-owner pair – although, again, this factor ought not to be considered separately from the wand wood, core and length, nor of the owner’s life experience and style of magic, all of which will combine to make the wand in question unique.
My deductions:
There is little we know about Bellatrix from the books but we do know that she is very proficient in the Dark Arts and inclined towards them, extremely powerful, quite temperamental, of unwavering loyalty, very dangerous with an impressive lack of conscience, and has a strong personality and dramatic style of magic which fits the descriptions here and they all echo each other. It's very likely that the rest would be true for her as well.
Since walnut wood favours witches and wizards who are extremely intelligent and are inventors and Bella is already portrayed as incredibly intelligent in the books — although some people keep conflating mental illness with lack of intelligence but that is, of course, utter nonsense — it's possible that in the past she may have had invented spells, potions, and other magical items of her own, something avant-garde. The text also indicates that she was a protean witch and knew a large variety of spells (which she herself stated in OOTP).
