Is there a bacherlors degree in applied science?

Yes, there is. They're not as common as "Associate in Applied Science" (AAS) degrees, but "Bachelor of Applied Science" (BAS) degrees do exist.

And BAS degrees suffer from much the same problem as AAS degrees: Not enough "lower-division general education" (LDGE) during the first two (freshman and sophomore) years.

In fact, many BAS programs are really just degree-completion programs for AAS degree holders so that said AAS degree holders, whose AAS degrees suffer from not enough LDGE, may nevertheless get a bachelors degree of some kind in only two years of study after the AAS degree.

The reason such is necessary is because AAS degrees usually contain much less -- sometimes as little as half -- the amount of LDGE as "Associate of Arts" (AA), or "Associate of Science" (AS) degrees...

...both of which, because they (AA/AS degrees) contain the same amount of LDGE as BA/BS degrees, typically count as the entire first and second (freshman and sophomore) years of said BA/BS degree. And so the AA/AS degree holder who transfers said AA/AS degree into the BA/BS degree may begin said BA/BS degree as a full junior, and then complete just the junior and senior years, and earn a BA or BS degree.

However, an AAS degree holder, who only has maybe half of the LDGE of an AA/AS degree holder, will find it very difficult to transfer his/her AAS degree into a BA or BS program... because, again, the AAS will be too deficient in LDGE to qualify as the first two (freshman and sophomore) years of the BA/BS. And so the AAS student finds himself/herself having to take sometimes as much as almost a year of full-time LDGE coursework in order to get "caught-up" with the BA/BS's LDGE requirements before s/he may be considered a full junior in the BA/BS program. The AAS transfer student, then, can end-up having to take almost three years to get the BA/BS, whereas the AA/AS student can do it on only two.

Many -- not all, but many -- BAS degrees were created so that AAS degree holders could get their bachelors in two years, just like that AA/AS degree holders. But the BAS is still deficient in LGDE compared with a BA/BS; and so the BAS may or may not be acceptable as requisite for entry into to a higher-level masters degree program (unless, of coures, it's a "master of applied science" degree... which I'm not even sure exists... I'd have to research it).

While there are BAS degrees which may be entered into at the freshman level, and then pursued for four years until completion, most BAS degrees are simply to help AAS degree holders get their both AAS and BAS in the same four years as AA/AS degree holders can get their both AA/AS and BA/BS degrees.

So the problem, then, begins at the AAS level. My advice is to never get an AAS unless you're absollutely, positively certain that that's the only degree you'll ever get. Ever!

If you think that there's even the slightest possibility that you'll one day pursue a bachelors, then stay the heck away from AAS degrees! Instead, get an AA or AS so that you can one day transfer it into a BA or BS. Otherwise, if you get the AAS, you'll be limited to either a BAS, or to having to take longer to get a BA/BS.