With new strings you need to make sure that they are not loose.
When you put new strings on you need to
1) Tune them up to pitch
2) Pull or "tug" each individual string gently (using all four fingers so you do not bend or pinch the string) away from the body of the bass a couple of times.
3) Repeat this process until the string stays basically in tune. It should take about 3-4 times doing this.
What happens is that there is slack around the tuning pegs and the wire that goes around the ball end. By doing this you remove this looseness.
Also when stringing the bass you want to make sure there is a good amount of string being wrapped around the tuning peg where each wrap is in contact with each other. This is why there is string and/or a single wire wrapped around the end of the string. This creates friction between the wraps and lessens the ability for it to move once in tune.
Also note before you cut the end of the string to put it on the bass you should bend the string a little more than 45 degrees and then cut the string about a half an inch past the bend. Since I'm assuming that you are using roundwound strings if you don't do this it will cause the wrap to loosen when you cut it.
So that covers the string tuning issue.
The bend in the neck is natural. You will need to have a slight bow in the neck. If you put a capo or hold down the string at the 1st fret and then use your elbow to press the string at the end of the neck you should be able to see the bow of the neck in relation to the straightness of the string. Take your right hand and tap the string around the 7th or 9th fret and you should feel and hear a slight click where the string touches the neck. The distance between the string and the top of the 7th or 9th fret should be just a little less than the thickness of a credit card. When you put a credit card between the fret and string it should touch both and maybe move the string a little. If it doesn't meaning that there is way too much space you will need to tighten your truss rod. If you can't fit the credit card then there is too much tension and you will need to loosen the truss rod.
However, the amount of relief (bow) and string height (action) is a personal preference. You just need to find what works best for you.
For example, I have extremely low action on all my basses where the neck is pretty much straight and the strings are as low as they can go. I like a little "sizzle" where the strings buzz a little when I play. Others though like the action and relief really high.
Hope this helps?
The scary part of studying Bird is that you are only seeing what he considered "normal" not challenging. Sadowsky Club Member #365 6 String Bass Club member #28 My YouTube Page