I have bought a fair few bats online and from overseas (as it was alot cheaper than buying here in Australia) -these include off the shelf bats and custom made as well - can't say I have been disappointed yet. I think if they have a good reputation that should alleviate some concern. Also if online sales make up a decent portion of sales for a shop then you would expect them to be pretty reliable as they have a reputation to maintain. I'd personally go with only the dedicated cricket stores though, as you are much more likely to get something you like - since the staff tend to be more dedicated and knowledgeable and also more responsive. Bigger sports stores that cater to all sports (eg Sports direct in the UK or Rebel sport for example in Australia), its much more of a gamble in my opinion so in this case I would like to visit and pick out a bat.
It also helps if you know exactly what you are after, as you can convey that to the sales person (assuming they are knowledgeable enough - which is why I would stick to dedicated stores only), they can usually find you something that is right up your alley.