Isn't is true that in most cases, both the ss and the s-set can be interchangeable in words such as Grusse and in most cases, modern (proper German, not necessarily Bayerish German) spellings are moving more toward the ss spelling?
Note: pardon the lack of proper German characters. I'm using an English keyboard and don't want to muddy the spelling waters further by using the accepted English spelling of u-umlaut being ue.
No, if you intend on learning standard Hochdeutsch, the ß plays an important function, which is assisting with pronunciation (and therefore is of great assistance to learners of the language). ß indicates that the previous vowel is long, ss indicates the previous vowel is short. The ß does not exist in Swiss Standard German, but I don't believe spellings are moving towards ss in Hochdeutsch. If in doubt by all means use "ss" however.
Oh and just some history, ß (ess-zett), literally "sz" is a ligature, which is the merger of the letters "s" and "z". Historically there was a long "s", exactly the same as the modern mathematical integration symbol (ſ). Combined with the standard symbol for "z" in cursive script, much like a "3", you get the ß shape.
What the others said. You can, however, substitute the "ß" with an "ss" and the umlauts with "ue", "ae" and "oe" if you're typing on a foreign keyboard and have absolutely no possibility of using the correct characters. But this is a makeshift solution and should only be done in exceptional circumstances. (Swiss Standard German is a different matter, but that has already been explained).