Blue decides to rape Bulma. For the first time in her life, the girl is
surprised her good looks backfired instead of helping her having it
her way. After that, depends on how soon Goku arrives. If he arrives
before Blue can rape Bulma, nothing changes. If Blue is really fast
(wink wink) and Goku arrives after he has raped Bulma, it's hard to
tell what kind of psychological problems the rape has caused her and
how it affects her future decisions.
Maybe she gets so depressed that she gives up everything in her life,
so she doesn't help the gang with her scientific knowledge, though they
can still get help from her father, so i don't think that really affects
the plot.
A more likely change is Bulma not wanting to couple with Vegeta, which
leads to a 'no Trunks' universe (i have described such a possibility in
an older thread, so i won't do it again). Also, maybe, when Androids
attack, she's not in the mood to try to save the world, so she does not
develop the time machine, which leads to Androids terrorizing the world
until they're absorbed by Cell.
If that version of Cell was predicted by the orcale fish to be the Super
Saiyan God, Beerus wakes up (later than in canon) and Cell becomes
his student. Not known whether U6/U7 tournament still takes place.
If it does, we also have to wonder: Does Zamasu view Cell as an inferior
mortal? If he does, considering there is no time machine, the Zero Mortal
plan succeeds.