Yes, this works - with a few caveats
First, as pointed out by KilrathSly, you will need to fail your save against Bestow Curse, in order to have the curse affect you. Note that you cannot voluntarily fail a save, even against your own spell.
Second, once you have your Bestow Curse up and running, note that it is a concentration spell. As such, the damage you take from the Life Transference has a chance of ending the Bestow Curse. Even at just 5d8, that is going to be more than 20 damage most of the time, so above a DC10 Con save.
Using a third level slot (Bestow Curse) to set up some reliable bonus healing might be justified depending on your party's class composition, but using a third level slot to try to combo and then making the save on your curse, or failing the save and then having the curse fall to lost concentration the first time you use it might not be a sound strategy.
Once past these hurdles, though, you are correct. With you as the target of your own curse, "your attacks and spells deal an extra 1d8 necrotic damage to the target". Since Life Transference says "You take 4d8 necrotic damage", it would actually do 4d8+1d8 = 5d8 necrotic damage to you. This satisfies its own condition of "the necrotic damage you take" - the extra necrotic damage from the curse has become part of the spell damage from the transference and is passed on as healing to the target.
One final caution, in your question you ask "will I heal the target of Life Transference for an extra 1d8?"
No, you will heal them for an extra of twice what you rolled for the extra 1d8 damage from the curse. You don't make a separate damage and healing roll. Rather, you make a single damage roll and the healing is twice that amount, without a roll.