Search and replace in bash using regular expressions

I’ve seen this example:

hello=ho02123ware38384you443d34o3434ingtod38384day
echo ${hello//[0-9]/}

Which follows this syntax: ${variable//pattern/replacement}

Unfortunately the pattern field doesn’t seem to support full regex syntax (if I use . or \s, for example, it tries to match the literal characters).

How can I search/replace a string using full regex syntax?