Each person's experience is a bit different.
I started on upright and later picked up 4-string BG. Later I transitioned to 5-string BG for few years before transitioning to 6-string BG. My #1 BG since about 1995 has been a Yamaha TRB6.
As has been suggested, put your 4-string BG in the case and leave it. You may be able to continue playing the upright, as it is different enough that it may not cause problems...but this depends on you.
I found boths transition slow and somewhat challenging. My belief is you use sort of a mental spatial map to nevigate the fretboard. This relates to what we call muscle memory. The idea is you intuitively know where to place your fingers without thinking about it too much...it's mostly automatic and subconscious.
IMHO if you pick up your 4-string BG, it will slow the transition because it either makes you use the wrong map or reinforces errors in whatever map you use.
It took me a few weeks to get comfortable with the extra string, but I would not say I was fluent. I had to think about it more, and I tended to get lost because my inaccurate automated process would take over. During this time I tried to focus more on the strings I was already familiar with, and play the extra string(s) only when absolutely necessary.
It took a few months before I started getting comfortable on the new string. I would stay it probably took about two years to regain all of the capabilities I had prior to the beginning of each transition. But getting comfortable on the new string(s) is not necessarily the end of the transition.
I would say it took at least a decade for me to really start thinking like a naturalized 6-string player. The extra strings give you more options for navigating the fretboard. To cover two octaves on 4-string, you need to shift up and down the neck. With a 6-string there is more tendency to play across the neck.
Now I can pick up a 4-string and 5-string and play. But I am most fluent on the 6-string. If I try to play a technically challenging line on a 4- or 5-string, I will need to stop more to figure out how to play it efficiently, rather than just doing it. Even worse, I find that the longer I play a 4- or 5-string, the more it degrades my fluency on 6-string. So I tend to spend the vast majority of my time on 6-string. I do try to play through my entire collection of basses a few times every year, but I don't play a 4- or 5-string for an extended time.
I also went through one additional transition. I originally used the same Simandl fingering system on upright and BG. But a few years after turning pro I decided to adopt one finger per fret on BG. So at this point I generally use totally different fingering system on upright and BG.
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