Sorry for the following longwinded response, I am also a 3 yr regional pilot and here is my recent experience on the difficulty of getting a slot. I think that really depends. Some units are higher in demand than others (due to location, etc. for example a unit in more populated and pilot-ful Florida or Texas is going to have more applicants than a unit in Nebraska). I have heard of units getting 100+ applications and narrowing down the interview pool to a dozen or so, to ultimately pick 1 or 2 candidates. I think those units that get 100 applications are typically fighter units. Then there are units that only get 20 applications. So, if you REALLY want this you can increase your chances by applying to every single unit in the country regardless of where they are located or what they fly.

I personally thought the hardest part about getting hired is doing all the footwork that is required to even get to the interview. When I first started this process years ago the guard/reserve units were going through BRAC and it was damn near impossible to find out any information. You have to be motivated. Since you don't have a recruiter working for you as for active duty, you have to figure out and do EVERYTHING yourself. This means finding out what is required, scheduling and taking the necessary tests (AFOQT, TBAS), putting your package together (different units require different packages and that is another thing you need to find out), finding out which units are hiring and then figuring out how to contact those units, and actually getting through to the right person to get the hiring info. There are websites you can use to find which unit are hiring (baseops and wantscheck are the two big ones I think) but the problem is that not all units advertise hiring on these websites. So if there is a unit that interests you, you just need to call them up and talk to the chief pilot to find out hiring info. There are several units that I never saw advertisements for their hiring anywhere, but when I called them up, the chief pilots told me they were hiring (they were all very nice and helpful by the way if you are able to get through to them.)

After all this is done, to actually get called for an interview, it's important to have a good package - AFOQT/PCSM scores, GPA, letters of recommendation, etc. - but those are also subjective to each unit because I have found units weigh their applicants differently. For example I applied to one unit and they told me specifically that the only thing they didn't like about my package was that my PCSM was too low in comparison to other candidates they were interviewing and they would talk to me if I could retake the TBAS and get the PCSM score up. The next month I got hired by another unit that never mentioned or asked me about ANY of that - AFOQT,PCSM,GPA - but instead focused heavily on me as a person.
The other way you can increase your chances of getting an interview/getting hired is enlisting in the unit and working your way up. You may be the most competitive off the street applicant in the pool, but if they already have one of their own enlisted guys who they know and like, you never even stood a chance. If enlisting is not possible (I don't know anything about this process), you can at least try to visit the unit and meet the chief pilot and the pilots. It's my personal opinion that units are more likely to extend interviews to applicants who have made the effort of visiting their unit. This should be easy for you since you can fly for free.

As for actually getting hired... I know several people who got hired on their first interview... and others who had many interviews before finally getting hired. I have a friend got hired by a fighter unit on his first application/interview ever! and he wasn't even enlisted. Another friend who tried for like 6 years, he would always get the alternate slot because there was always the one dude who was prior enlisted that got the primary. I say if you really want this, persistence will pay off sooner or later. (as with most things in life I guess?)