"I had not lived without you."
Translation:Jag hade inte levt utan dig.
For one thing, the construction would be hade inte bott. bodde is the past tense form and bott is the supine, which is used to form the present and past perfect. For the verb used here, levde is the past tense and levt the supine.
Also, since bo only means 'live' as in 'reside', the sentence would be a bit strange, or stranger, with bott.
I think it makes more sense with "bott" than with "levt". In that case, perhaps someone has turned 18 and moved off to college. Speaking with their former family members, they may say this sentence with "bott" to explain their hardships, happiness, etc... With "levt", I'm not sure what the sentence is supposed to mean.. perhaps that they didn't know what they were missing until they met that person, and now they are truly living life to its full potential?
The translation with levt means that you don't know how to live without the other person; life would be very hard, not so bright and happy.
A translation with bott needs a location, I think: här, i Stockholm. The other person helped you with the move or with finding the house.