Long-ish answer warning! Here's a summary:
The only guaranteed-to-be-safe method of travelling to and from Corregidor:
- Sun Cruises Ferry which has trips to and from Manila and also a ferry to Bataan.
If you're ok with less-safe methods that could be less expensive, try:
- Pump boats from Mariveles: (text 09206480486 or 09277904684)
And here's one thing to definitely not try:
- Fishermen's boats from Mariveles: (note: this is illegal)
Read on for a detailed explanation of each:
Firstly, the most direct way to travel to Corregidor from Bataan is via Manila. Since Corregidor Island is privately owned, they have an agreement with Sun Cruises, which is the only company that organises Corregidor Island tours (that is to say, they have a monopoly). From Bataan to Corregidor it takes nearly four hours. To get from Corregidor to Bataan, OP found a 2011 site that suggests that:
The Sun Cruises [ferry] sometimes goes directly to Mariveles, Bataan [from Corregidor]. If you will be starting at Clark Airport [and don't want] to go by Manila's chaotic traffic, I would suggest Baler, Aurora or Sagada, Mountain Province. These are 2 of the best places [that are good] to go to North Luzon.
However, that information could be outdated and I cannot find anything else online about it.
Further, since the Sun Cruises company has a monopoly on transportation to the island, their services are sometimes subpar. The Sun Cruises ferry from Manila to Corregidor is frequently cancelled (even on the day!) due to a lack of passengers.
If you don't want to do that, there are multiple ways you can go around it. As per this site, if you don't want the price of the Sun Cruises ferry or want to get to the island early or late, you'll have to get a boat. However, you mentioned that you don't want to do that, but for other people, it still may be a viable option.
This site (this site is also good!) suggests a DIY approach to getting to Corregidor from Mariveles:
[If you're travelling from Mariveles to Corregidor, you can] go to Villa Carmen beach resort at Barrio Cabcaben, Mariveles. Text [these] numbers: 09206480486, 09277904684. They are pump boats that go to Corregidor on a daily basis. [They have] a fare of P2,500 - P3,000 per round trip [and they] start in the morning. [Each boat can] accommodate [eight people], [and you] pay upon the return trip.
However, if you're worried about safety, the pump boats could end up not being your best option:
Those pump boats are not accredited and not equipped to handle tourists. Transporting people to Corregidor is not the main source of their livelihood.
We're far from the safe options now, but there are still other ways to get there. If you're ok with breaking the law (of course you're not! However, hypothetically, if you could entertain the idea), there's another option: fishermen's boats.
The fishermen are use[d] to being approached [regarding their] brightly painted traditional but motored outriggers. [The quoted cost] is 3500php for groups of up to 8 people. [This is truly] an authentic experience, [but it's] no luxury cruise: don't do this [if you're] injured. [I found it fine even] in adverse conditions [that the passengers] are subject to in small unsheltered boats. They give you life jackets for a reason . The fishermen crew will wait for you to return in 4 to  hours: they like to return about 3 or 4 pm.
However, note that this is at least somewhat inadvisable: if you intend to take this route, note that (as per the same site):
If something bad happens to you, your travel insurance or health insurance won't cover it because, again, it's illegal.
Usage of this transport encourages fishermen to break the law: they could land in jail. Many of them are uneducated and may not know the consequence of bringing tourists to Corregidor.
Thus, I add this option not as a truly viable one but so that if you ever want to go to Corregidor you know to not choose this option.