I tend to agree with PaulCannon above in that using a tuner for all notes is mostly for the beginner. A cheap little Chinese watch-sized clip-on electronic tuner will do this well. Even then ASAP go over into aural training and tuning the bass by harmonics.
Most people can clearly hear a 5th, Octave and 10th based on the open D as tonic, either alternating between D and the other note or playing them as double stops.
Many other TB members believe in playing scales to D as a drone. I don't! The electronic drone or tuner, like the strobe tuner, is an external crutch (support) that I react to, rather than being pushed hard enough to pre-hear and aim for the notes that I am about to play.
I would rather carefully hear the scale as two tetrachords, the basic building blocks of a structure (Scale comes from the Italian word Scala, meaning Ladder) that is confidently applied to any chosen tonic note. Each group has the intervals Tone Tone 1/2 Tone with a Tone in the middle between groups. Pause slightly between each group and repeat octaves. This creates more "landings" in the long "flight of stairs" called the Major scale over three octaves and makes it much easier to stay in tune throughout. Set aside a quiet time to examine placing the two middle notes E and F sharp in between D and G, then B and C sharp between A and octave D. Try doing this in the dark to heighten your senses. Then repeat the process for the adjacent E flat scale, then any scale, then both forms of minor scales, then arpeggios. Pre-hear notes coming just as though you are aiming darts to hit a bullseye every time.
The level of intonation you can achieve in your practice alone at home might be called Absolute Pitch. As soon as you play with someone else you need good Relative Pitch, because for any number of reasons you have to be able to adjust your tuning quickly and accurately. The piano can't adjust to you so tune your open strings to the same-name notes piano around the middle of the keyboard. Try to play duets, trios, quartets with other bassists and instruments, and chamber music where you are the only bass. This will boost your confidence in smaller musical settings.
Fitting into an orchestral Bass Section is initially not easy. Within the rough-and-tumble you have to find your voice and tread a tightrope between playing too loud and "leading from the back desk" or playing too soft to hear yourself, risking being " a rotten apple in the barrel" that undermines the section result. You have to be able to recognise when you are right and adjust quickly if you are wrong. This goes for rythm, bow length and direction, timing entries and pizzicato, and style etc too. Your ears and eyes are constantly scanning. Being absolutely note-sure and finger-sure of your music at home first is a great help.
Finally, the better the other players in the section are the easier it is to play in tune with them, because you can hear a definite centre to each note and the section sound becomes bigger and more important than each individual player. Remember that each one of them has had to go through the same process and will be understanding if you make mistakes.
Have courage!
DP