The reality of the language is such that both forms are used, on both sides of the Atlantic, but the bare-infinitive form is clearly preferred, as the stats from the Corpus of Contemporary American English (COCA) and the British National Corpus (BNC) illustrate:
COCA BNC
all you have to do is [inf] 842 72
all you have to do is to [inf] 17 20
The preference does not change if all is replaced with what, if an adverb is introduced before the infinitive, or if a different pronoun is used instead of you. However, what also does not change is that the variant with to at least exists. (A peculiar exception seem to be she and it; negation is another interesting case, but the sample size is sadly too small for those). Sometimes the ratio is a mere 1:60, but other times it's not anywhere as cut and dry. Here are all the stats I have compiled so far:
COCA BNC
all you/we/they/I have to do is [inf] 842/206/68/62 72/27/9/8
all you/we/they/I have to do is to [inf] 17/ 3/ 3/ 5 20/11/4/2
all he/she/it has to do is [inf] 105/40/11 5/3/1
all he/she/it has to do is to [inf] 6/ 0/ 0 2/1/0
all you/we have to do is [adv] [inf] 9/5
all you/we have to do is to [adv] [inf] 0/0
all you/we/they/I have to do is not [inf] 1/1/1/1
all you/we/they/I have to do is not to [inf] 0/0/0/0
what you have to do is [inf] 59 8
what you have to do is to [inf] 11 4
what you have to do is [adv] [inf] 8 1
what you have to do is to [adv] [inf] 1 0
So if you want to be on the safe side, bare infinitive certainly is the way to go. It also happens to be the more logical choice, as demonstrated by FumbleFingers in his answer. But we can't label the other option ungrammatical, and its existence can be explained logically as well, as metanalysis.