When you first join the DB, Astrid says it's not unusual for members to serve time. She also said you could go to Riften and seek out the Thieves Guild. They'll remove the bounty for a price.
I like to poison frenzy the groom into murdering the bride, drink an invisibility potion, and then prep a master Calm spell to make everyone nice and happy again.
Or go all Werewolf and just eat the bride. That works too.
Drop the gargoyle and immediately take an invisibility potion or eat vampire dust?
Personally, I make sure to have enough money to pay my bounty.
At best, make sure you are part of the Thieves-Guild and have done your special-quest for Solitude before.
On the other side, playing so far the Thieves-Guild may be annoying for someone who just want to play the Dark-Brotherhood.
That is what she tells. But in game, as member of the Thieves-Guild, you just get a dialog to bribe the guard. Depending on your money and speech-skill, the guard will clear you bounty or just look away.
But it is an art of it's own, to join the Dark-Brotherhood without joining Thieves-Guild.