Mini Dachshund in heat for first time: how long does it last, when is she most fertile (we don't want her bred), and is there a usual amount of time between when the bleeding stops and her heat is over?

Her second or third heat is the best.

Heats usually last 7-14 days, most fertile in the first 3-4th day and two days after heat, best way to check is to ask your regular vet to look at her vaginal smears to determine weather estrus has ended. To prevent pregnancy don't leave her alone with any male dogs while unattended. ( I'm a vet tech so I do recommend spaying your dog)

A heat or season lasts on average 3 weeks, or 21 days.

The most fertile days are around days 8-12 .

Bleeding may only occur for a week towards the beginning of the season, but once bleeding ceases (around day 8) this is actually when the b*tch is ready to mate, NOT finished contrary to popular belief. The b*tch is still capable of becoming pregnant for 2 more weeks after that.