Minor backstory spoilers for a handful of Bells.
The overwhelming majority of Bells have a Charlie and a Renée for parents. Charlie and Renée are templates-proper, but are not either of them very context-dependent - Bell grandparents are often only template-cousins of each other (though the Earth ones would be most similar, allowing for variations like Stella needing to have room for Elias Frobisher in there and so on). Bells will have these standard parents even if one of them is going to die when the Bell is young (Rose, Etty, T'Mir) or if she's going to leave their presence when she's young (Aegis, Tab). However, in cases when a Bell's biological parents are totally irrelvant to her development from earliest infancy (e.g. Katie, Loki) or don't exist for the species (Promise) the biological parents are not Renée and Charlie instances at all. Inheritance of traits from the parent templates works causally, not metacausally. Loki doesn't have a Renée and Charlie anywhere, not even as frost giants who she's never met, but the template and its traits - wherever those traits normally sprout - are still operative in her; likewise Katie. An exception to this is Rapunzel, who per Tangled movie canon is collected from her parents as a baby and doesn't meet them during her entire upbringing but still has a Renée and a Charlie as her bioparents. Ara is also a weird case because she's a clone of Izzy, but Izzy's parents are typically parental to Izzy.
If I'm going to make a Bell something that is unusual and inherited, it will usually be from the Renée's side of the family (Amariah the witch, Angela the angel, Chi the airbender, Kiri the Ardelay, Maurabel the mage, Phix the sphinx, Mira's fairy godmother, Raven the half-blood witch) but this is not a guarantee (T'Mir's dad was the Vulcan; Lorica inherits her cape status from her dad) and if I'm making the Bell something that is not locally unusual, or wouldn't have shown up in the family before, it can be either (Clarity's dad is a unicorn like her and her mom is a pegasus; I haven't even decided which side of the family contributed Aurora and Lexi's mage genes). The ones who are born royal (rather than invented/adopted/married/ascended royalty) are Cymbeline and Rapunzel. In his case his mom was a princess and his dad was a knight who won her hand in some manner I have yet to specify. In Rapunzel's case her dad is the one who was locally royal all along but her mom was a foreign princess. If I have cause to make further prince(ss)ly Bells there is a weak attractor for the mom to be the source of the royalty if it's only one side of the family.
Now, in terms of the raw material that makes a Bell instance, let's break down what each parent supplies.
Moms/Renées:
- Raw intellect, G-factor, sheer mental horsepower. Renées are very smart. They just don't have personalities which leads them to take advantage of this for more than short periods at a time - not enough attention span or ambition.
- Curiosity - again limited very much by attention span. It occurs to Renées to wonder, but not to put inconvenient effort into finding out.
- Relationship to native culture. Like Bells, Renées bear obvious stamps of where they grew up and the norms of those places, yet retain a balanced open attitude towards other cultures they encounter.
- Initiative and energy - the thing that lets them transition instantly from "it might be nice if" to "I could do this" to "doing this now". Limited again by attention span and ambition; Renées mostly use this to pick up new hobbies and travel.
- Creativity, imaginativeness, the streak of whimsy Bells materialize when encouraged by their environments.
Dads/Charlies:
- Methodical and careful habits of thought. In Charlies, this is limited by smarts (Charlies aren't stupid, but they're not as smart as Renées) and imagination (of which Charlies have little).
- Sticktoitiveness/persistence. The ability to keep showing up and working on the thing even if it's not endless fun.
- Unshakeable moral center. Renées aren't prone to immorality, but they run more on habit and innate niceness (Bells don't, mostly, have Renéelike innate social niceness; they have moral niceness) while Charlies run on principle, and Bells have the Charlie version.
- A thing I'm calling "recentering". Charlies don't do it unless they have to and will resist having to (whereas Bells will actively seek it), but if you force a Charlie to acknowledge that there's aliens or magic or other universes or otherwise things that are beyond his present comprehension, he will adjust, once, and then be OK with that.
- Civic responsibility; the feeling that there are things to be done for other people which you ought to do because you just plain ought.
- Introversion.
Personality traits that Bells have as a template that don't have an obvious parent source:
- Intense introspection as a core drive, esp. via recording of thoughts in an outside medium
- Taking moral center to logical, extreme, culturally unusual conclusions e.g. anti-deathism
- Self-centered attitude (both parents are only fairly ordinary amounts of self-centered, Renée more than Charlie but not this much)
- Intrinsic desire for arbitrary amounts of power (the civic responsibility thing taken to its logical conclusion does not fully explain this aspect of Bells)
- Sarcastic and flippant tendencies
- Intense attachment to romantic partners of choice once selected (Renées obviously don't have this; Charlies don't have it this much, or the standard version would try to move with Renée when she evinced a desire to leave because Forks is boring)
For comparison, the Bellsiblings:
Alexes are, like Bells, pretty mixy, but it's a less potent trait combination. They have Renée-sourced creativity, extroversion, and cognitive carelessness, Charlieish "recentering" traits without the Charlieish active resistance to making the transition, Charlie's tendency to satisfice instead of iterating or optimizing, Charlie's emotional reserve, a medium-sized attention span, modest intellects, sporadic initiative, and the Charlie ability to put another person unqualifiedly first (though their ability to also happily substitute a Bell's judgment for theirs is all their own; they have kind of limited doses of both social and moral niceness and find it easier to work with a readily-available supply that happens to reside in someone else).
Sophs are mostly like Renées with better attention spans, less G-factor, more initiative, and Charlie's ability to be a good listener when called upon. (Typically, Alexes do better in school than Sophs, A's-and-B's to B's-almost-always, but they're about the same amount of smart; Alexes just lean harder on their Bells than Sophs; Sophs are more independent in general.)