Bethany's starting approval rating is 
(+50); she will receive an unavoidable (+10) in prologue ( (+15) if the aggressive dialogue with Wesley is chosen). This makes it virtually impossible to maximize rivalry with her.
Friendship
Friendship with Bethany can generally be earned through acts of kindness, by siding with mages or by supporting family. Bethany is a faithful Andrastian and also distinctly opposed to blood magic, so rebuffing demons and opposing blood mages will earn friendship as well.
Prologue
- The Destruction of Lothering: As a non-mage, choose the Aggressive response to Wesley's threatening of Bethany, upon meeting Aveline for the first time for
(+15). All other choices garner (+10).
Act 1
- Bait and Switch: Directly defend Bethany at the end of the quest for (+5)
- Birthright: By simply entering the vault in the Amell Estate basement you gain (+15). A further (+10) can be gained upon returning to Gamlen's House with Grandfather's Will and speaking with Bethany by choosing the friendly response on the second dialogue wheel.
- The Deep Roads Expedition: Take Bethany on the expedition (+10)
- Enemies Among Us: Ask for Bethany's assistance in breaking Idunna's compulsion (+5)
- Long Way Home: When Merrill opens the barrier with blood magic, choose the Aggressive option, "The demon, you mean." for (+5)
- Loose Ends: (Athenril/Smuggler Path) Let the young boy start a new life with his sisters by letting him have the loot. (+15)
- Magistrate's Orders: Kill Kelder (+5)
- Portrait of the Past: Giving Bethany your mother's portrait (found in a chest in the Amell Estate basement) back at Gamlen's House results in (+10), regardless of dialogue choices.
- Shepherding Wolves: Accept the quest from Sister Petrice (+5)
- Shepherding Wolves: Refuse to hand over Ketojan to the Arvaarad (+10)
- Tranquility: Promise Lirene you won't harm Anders (+5)
Tranquility: Upon leaving Lirene's Fereldan Imports you will be approached by Angry Fereldan; choosing the response, "We're on the same side." (available to a Diplomatic Hawke) instead of deferring to Bethany results in (+5). Alternatively, deferring to Bethany will result in the same approval gain, though Aveline Vallen does not gain (+5) also.
Tranquility: When talking to Anders, choosing "You want me to fight templars?" yields (+5)
Tranquility: When asked to kill Karl, choosing "Do as he asks" yields (+5) - Wayward Son: If Hawke choose the option "make up for your neglect" when speaking with Vincento. (+5)
Legacy DLC
- Legacy (quest) If you side with Larius (+5).
- After defeating Corypheus and returning to your house, talking with Bethany and choosing the diplomatic or sarcastic options yields (+5)
Rivalry
Rivalry with Bethany can generally be earned by choosing aggressive responses, by siding against mages or by exploiting Fereldans.
Act 1
- Act of Mercy: When talking to Grace, choosing "I won't help you" yields (+5) When talking to Sir Thrask at the end, turning the mages into the Circle yields (+10)
- Long Way Home: When Merrill opens the barrier with blood magic, say "It did help us". (+5)
- Bait and Switch: At the end of the quest, agree with Fenris by saying, "I know the risks" of cooperating with a mage. (+5)
- Birthright: After finishing the quest, talking to Bethany and choosing "This will never be home" leads to (+10)
- Enemies Among Us: When talking to Knight-Captain Cullen during the end of the quest, Hawke can receive up to (+15)
- Shepherding Wolves: Refuse the mission (+5)
- The First Sacrifice: If you sleep with Jethann you receive (+5)
- Magistrate's Orders: If you let Kelder live (+5)
- Tranquility: After leaving Lirene's Imports, take an aggressive stance against the Fereldans (+5)
Tranquility: When asked to kill Karl, choosing "Don't kill him" yields (+5) - The Deep Roads Expedition: Leave her behind at home (+10)
- The Deep Roads Expedition: If you bring Bethany to the Grey Wardens (+15)
- Wayward Son: When you talk to Arianni and choose the aggressive responses (+10)
- Wayward Son: Sending Feynriel to the Circle (+10)
Legacy DLC
- Legacy (quest) If you side with Janeka (+5)
- After defeating Corypheus and returning to your house, talking with Bethany and choosing the aggressive option yields (+5)