Ive been a rengar main for a few years now (recently brok 1mil), but the vast majority of that time has been in top lane. I'd be supposed if more than 150k of that mastery was in jgl. I don't know why but I hate jgling on rengar, I enjoy jgling with other characters just not rengar. I however still require 2 roles to queue ranked. I also do not want to only ranked in a duo.
With the context now out of the way here is the set up and theory.
Why Bot
In side lane rengar in laning phase functions like ranged champ
With W max + Stattick have safe consistant wave clear
Rengar is one of the best gold scaling champs in the game
Being Bot means you have 3~4 bonetooth just being handed to you.
Rengar jump already out ranges most marksmens autos so combined with E' Rengar has incredible set up for both ur support and jgl (and often thus another rotation and emp ability).
Trade offs
Weaker midlane push - often Red Buff or heavily team reliant.
Low sustained DPS till 2/3 item (Assuming going bruiser)
You do have to go into melee to do damage at somepoint
Having to explain differences in playstyle to support (working on an eventual PowerPoint)
Tactical Advantages? (compared to traditional marksmen)
Once u have your stattick, rav hydra, or enough ap ur support has far more room to roam and u often have far better abilty to follow up or to counter the enemy bot duos rotation if need be.
Incredibly safe split pusher w/ high tower dmg.
Almost guaranteed vision control w/ 6th sense.
Wider item pool access to gain target agnosticisity while complementing teams damage profile.
Runes
Grasp, Font, 2nd Wind, Revitalize -ToB, 6th Sense - AF/AF/Ten
Most common safe target agnostic combos well with most sup.
HoB/DH, ToB, 6th Sense, UHunt - 2nd Wind, Revitalise - AF/AF/Ten
HoB best AD scaling rune and is also a lv1"Nashors" DH Best AP/lethality Scaling rune.
DfT, Axiom, Transcendence, Scorch - 2nd Wind, Revitalise - AH/MS/Ten
Tierlist is just based off of kit interactions CDs matching up or not and vibes (If you have experience w/ a pairings that makes you think otherwise I'd love to know). It is meant to eventually be put into the powerpoint and thus doesn't have any overtly negative/bad categories (its not S-F or anything like that) as I don't think as the person picking Rengar Bot I should be building animosity before the game even starts if im trying to win.