hi! i think i can help. here's some context nobody asked for.
The number you're adjusting is the beatLength value. It accounts for the length between beats in ms. ∞bpm implies that there are 0ms in between beats, but osu! can't actually handle a beatLength of 0. However, you can trick beatLength into being 0 by having a very, very small number. In this case, 1E-298 (or roughly, 0.00000...(a couple hundred 0's)...0000001).
unfortunately, i believe that this means that a bpm of -∞ is impossible, as setting beat length to -1E-298 will also round to a beatLength of 0. i don't think that "negative 0" is a value osu! (or humans) can understand.
vvvv actual answer vvvv
Luckily, your second proposal is entirely possible. Just as having ∞bpm implies a beatLength of 0, having 0bpm implies a beatLength of ∞.
Again, osu! can't have a beatLength of ∞, but guess what! You can trick beatLength into being ∞ by having a very, very big number! I love this game.
If you set the beatLength to 1E+298 (or roughly, 10000...(a couple hundred 0s)...000), you should receive a bpm of 0. Of course, this is entirely useless, but it appears in the song select screen, and thats neat enough for me.
Hope this helped.