I have a matrix of Beta values with CpGs (18500 CpGs) as columns and samples as rows called methyl. I am making a GenomicRatioSet using minfi before using it on the bumphunter function applying the code below:

GRS <- makeGenomicRatioSetFromMatrix(t(methyl), what = "Beta")

Then I am also turning Beta values to M values and storing in this object using the code:

assays(GRS)[["M"]] <- getM(GRS)

However, when I run bumphunter with same parameters on M values and Beta values like this:

with_beta <- bumphunter(object = GRS, design = mod, cutoff=0.3, B=0 ,type = "Beta") 
with_M <- bumphunter(object = GRS, design = mod, cutoff=0.3, B=0 ,type = "M")

Turning Beta to M values introduces some NaNs but bumphunter founds and removes them. The problem is with beta values it founds 57 bumps and with M values it founds 10659 bumps even though it removed some values. Is it normal to get this much of a difference between Beta and M values? What am I doing wrong?

It's due to two things. First, you are asking for a larger difference when using beta values than M-values (0.3 is a 30% change in methylation when using beta values and is a 1.23-fold change (or about 23% change) when using M-values). Second, beta values are strictly bounded on [0,1], and tend to be near the bounds for most CpG sites. A change of 0.05 -> 0.1 in beta values is only a change of 0.05, which is far less than your cutoff, but is a 2-fold change which is far larger than your cutoff when using M-values.