I think, there is no sufficient documentation available for the APIs. According to the code here 3, the probability is taken as 0.5 in case if there is no parameter provided for p.
If you change the code as below, it seems to be giving same functionality as non in-place operator.
import torch
import numpy

torch.manual_seed(seed=1)
torch.cuda.manual_seed(seed=1)
a=torch.zeros((10,))
print(a.bernoulli_(a).numpy())

Note the parameter passed to bernoulli_(),