If you can play upright, you should be able to play fretted bass guitar. That doesn't mean everything you do on upright is optimal for bass guitar, only that in general it will work with minor adjustments.
As you develop, your technique on each instrument will likely diverge considerably. I originally used Simandl fingering on bass guitar. However a few years into being a pro, it started becoming increasingly apparent that I would benefit from using one finger per fret (OFPF) on bass guitar. I also transitioned from 4-string bass guitar to 5-string and then 6-string. So know I use totally different fingering system on bass guitar and upright.
I never could get comfortable on fretless bass guitar. I think part of the reason is because I use OFPF. My hand is not big enough to use OFPF on a fretless and I refuse to give it up. My solution was to get an electric upright. I felt immediately at home on the electric upright.
I never had any problems switching between fretted bass guitar and one of the uprights. I do find switching between upright and electric upright challenging in some situations. When functioning as part of a rhythm section, where I am loud enough to hear clearly, I can adjust intonation on the fly. When playing in a classical style as part of a bass section, you don't necessarily hear well enough use to your ear. Instead you have to really fine tune the calibration of your hand so that you can pretty much nail it. So the solution for me when I needed to play classical was to put away the electric upright and practice Simandl so my intonation would settle.
I can't say if I would have the same problem switching between fretless bass guitar and upright. My electric upright had approximately the same scale as an upright (~42") Bass guitar is usually around 34-35." Maybe that's enough of difference...I can't say.
I started on upright in 8th grade orchestra. Actually I crossed from viola. I played in a local youth symphony and also participated in annual All City and All Region orchestras. As a Freshman in high school I also played in big band. I played upright acoustically and there was a bass guitarist who used an amp at the same time. This allowed me to learn quite a bit, but you really couldn't hear me.
Junior year I dropped out of the school music programs. Then meant I was not eligible for the Youth City or All City or All Region. However, I was asked to play in a local university's big band. I borrowed a really crappy short scale bass guitar. The bass lines were written out for some of the music, but a large percentage of the music only gave chord symbols, which means you are expected to improvise a bass line. I did not know theory yet, so this was not viable. The big band director gave me sheet music and recordings for all of the songs. So basically I did record lifts of the bass parts.
I wound up majoring in music in college. The school had discontinued its commercial music program the semester before I started; so I was in a classical track. The music theory courses I took basically harmonized major and minor keys and focused on the rules of voice leading. Harmonization is basically generating the diatonic 7th chords that belong to a key. Learning the keys, key signatures, and diatonic 7th chords cold is really the foundation of improvising a bass line over chord symbols. So the theory classes gave me everything I needed to start figuring out how to improvise over chord notation. I bought one of the old black-market Real Books and one of the schools guitar instructors mentored me once or twice a week.
I have taken quite a few lessons on upright. I have never taken a lesson on bass guitar. You need a certain level of technique to play jazz. But it is far more important to have a foundation in music theory and develop a vocabulary that you can apply over chord changes. Basically you learn to play the instrument, then you learn theory, then you learn to apply the theory in real time on the instrument. Listening to and copying great players is a very useful activity to help build your vocabulary.
This is getting TLDR. I could probably keep writing and getting more detailed. But hopefully this is enough to give you an idea on how to proceed. There is nothing wrong with taking lessons on upright or bass guitar, but IME lessons usually focus on pedagogy/technique. In order to play jazz, you need a different type of instruction. You could major in music or take lessons that are focused on giving you the necessary foundation in music theory.
The music for high school level big band generally will have a written out bass line. College level and pro level big bands may have a few pieces with written out bass lines, but you really need to be able to read chord symbols and create your own bass line in real time.
Jazz combo is a bit different. Ideally to play in jazz combos you will have a bunch of head charts memorized so you don't need any sheet music to guide you. I am not an authentic jazzer, so while I do know a few songs, it's nowhere near enough to play in a good jazz combo. I do very well with Real Books gigs were I can use my crutch

.