The fixed price wariness tonyedgecombe mentions is real. Early in my career I'd quote hourly because it felt "fair" - but what I learned is that clients who want fixed pricing often have way more context than you do about the problem's difficulty.

Flipped it around now. If a client is eager for fixed pricing on something that seems simple, I dig deeper. Usually there's a reason three other contractors already passed on it.

The psychological bit about being embarrassed to invoice is spot on though. Took me years to stop treating invoices like I was asking for a favour. The framing shift that helped: you're not asking for money, you're confirming a transaction that was already agreed.